35th@MSC2020-3：分析学@20260125
| 26-XX Real functions [See also 54C30] 26-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to real functions 26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions 26-02 Research exposition (monographs, survey articles) pertaining to real functions 26-03 History of real functions [Consider also classification numbers pertaining to Section 01] 26-04 Software, source code, etc. for problems pertaining to real functions 26-06 Proceedings, conferences, collections, etc. pertaining to real functions 26-08 Computational methods for problems pertaining to real functions 26-11 Research data for problems pertaining to real functions |
26-XX 实函数 [另见 54C30] 26-00 与实际功能相关的通用参考文献（手册、词典、参考书目等）
26-01 实函数相关导论性阐述（教材、辅导论文等）
26-02 关于实函数的研究文献（专著、综述文章）
26-03 实函数的历史 [另请参阅第01节中的分类编号]
26-04 与实际功能相关问题的软件、源代码等
26-06 与实函数相关的会议记录、会议论文集等
26-08 实函数相关问题的计算方法
26-11 实函数相关问题的研究数据
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| 26Axx Functions of one variable 26A03 Foundations: limits and generalizations, elementary topology of the line 26A06 One-variable calculus 26A09 Elementary functions 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48] 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 26A16 Lipschitz (H¨older) classes 26A18 Iteration of real functions in one variable [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25] 26A21 Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems [See also 28A15] 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives 26A30 Singular functions, Cantor functions, functions with other special properties 26A33 Fractional derivatives and integrals 26A36 Antidifferentiation 26A39 Denjoy and Perron integrals, other special integrals 26A42 Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX] 26A45 Functions of bounded variation, generalizations 26A46 Absolutely continuous real functions in one variable 26A48 Monotonic functions, generalizations 26A51 Convexity of real functions in one variable, generalizations 26A99 None of the above, but in this section |
26Axx 单变量函数 26A03 基础：极限与泛化，直线的初等拓扑学
26A06 一元微积分
26A09 基本函数
26A12 函数的增长率、无穷阶函数、缓慢变化函数 [另见 26A48]
26A15 一元实函数的连续性及相关问题（包括连续模、半连续性、间断性等）{关于由傅里叶系数决定的性质，参见42A16；关于由逼近性质决定的性质，参见41A25、41A27}
26A16 莱普希茨（H¨older）类
26A18 一元实函数的迭代 [另见 37Bxx、37Cxx、37Exx、39B12、47H10、54H25]
26A21 实函数的分类；集合与函数的Baire分类[另见03E15、28A05、54C50、54H05]
26A24 分化（一元实函数）：一般理论、广义导数、中值定理[另见28A15]
26A27 无微分性（不可微函数，不可微点），不连续导数
26A30奇异函数、Cantor函数及其他特殊性质函数
26A33 分数导数与积分
26A36 抗分化
26A39 丹乔伊-佩龙积分及其他特殊积分 26A42 莱曼、斯蒂尔杰斯和勒贝格型积分 [另见 28-XX]
26A45 有界变分函数的泛化
26A46 一元绝对连续实函数
26A48 单调函数，推广
26A51 一元实函数的凸性，推广
26A99 上述均非，但本节适用
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| 26Bxx Functions of several variables 26B05 Continuity and differentiation questions 26B10 Implicit function theorems, Jacobians, transformations with several variables 26B12 Calculus of vector functions 26B15 Integration of real functions of several variables: length, area, volume [See also 28A75, 51M25] 26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) 26B25 Convexity of real functions of several variables, generalizations 26B30 Absolutely continuous real functions of several variables, functions of bounded variation 26B35 Special properties of functions of several variables, H¨older conditions, etc. 26B40 Representation and superposition of functions 26B99 None of the above, but in this section |
26Bxx 几个变量的功能 26B05 连续性与分化问题
26B10 内隐函数定理、雅可比行列式、多变量变换
26B12 向量函数的微积分
26B15 多变量实函数的积分：长度、面积、体积 [另见 28A75、51M25]
26B20 多元实函数积分公式（斯托克斯、高斯、格林等）
26B25 多变量实函数的凸性，推广
26B30 多变量绝对连续实函数，有界变差函数
26B35 多变量函数的特殊性质、H¨older条件等
26B40 函数的表示与叠加
26B99 上述均非，但本节
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| 26Cxx Polynomials, rational functions in real analysis 26C05 Real polynomials: analytic properties, etc. [See also 12Dxx, 12Exx] 26C10 Real polynomials: location of zeros [See also 12D10, 30C15, 65H05] 26C15 Real rational functions [See also 14Pxx] 26C99 None of the above, but in this section 26Dxx Inequalities in real analysis {For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15} 26D05 Inequalities for trigonometric functions and polynomials 26D07 Inequalities involving other types of functions 26D10 Inequalities involving derivatives and differential and integral operators 26D15 Inequalities for sums, series and integrals 26D20 Other analytical inequalities 26D99 None of the above, but in this section |
26Cxx 多项式，实分析中的有理函数 26C05 实多项式：解析性质等[另见12Dxx、12Exx]
26C10 实多项式：零点位置 [另见 12D10、30C15、65H05]
26C15 实有理函数 [另见14Pxx]
26C99 上述均非，但本节
26Dxx 实分析中的不等式 {关于极大值函数不等式，参见42B25；关于泛函不等式，参见39B72；关于概率不等式，参见60E15}
26D05 三角函数与多项式的不等式
26D07 涉及其他类型函数的不等式
26D10 涉及导数及微分与积分算子的不等式
26D15 等式、级数和积分的不等式
26D20 其他分析不等式
26D99 以上均非，但本节适用
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| 26Exx Miscellaneous topics in real functions [See also 58Cxx] 26E05 Real-analytic functions [See also 32B05, 32C05] 26E10 C∞-functions, quasi-analytic functions [See also 58C25] 26E15 Calculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx] 26E20 Calculus of functions taking values in infinitedimensional spaces [See also 46E40, 46G10, 58Cxx] 26E25 Set-valued functions [See also 28B20, 49J53, 54C60] {For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx} 26E30 Non-Archimedean analysis [See also 12J25] 26E35 Nonstandard analysis [See also 03H05, 28E05, 54J05] 26E40 Constructive real analysis [See also 03F60] 26E50 Fuzzy real analysis [See also 03E72, 28E10] 26E60 Means [See also 47A64] 26E70 Real analysis on time scales or measure chains {For dynamic equations on time scales or measure chains, see 34N05} 26E99 None of the above, but in this section |
26Exx 实函数中的杂项问题[另见58Cxx] 26E05 实解析函数 [另见 32B05、32C05] 26E10 C∞函数、拟解析函数 [另见 58C25]
26E15 无限维空间上的函数计算[另见46G05,58Cxx]
26E20 无限维函数的微积分
空间 [另见46E40、46G10、58Cxx]26E25 集值函数 [另见28B20、49J53、54C60] {关于非光滑分析，参见49J52、58Cxx、90Cxx}
26E30 非阿基米德分析 [另见 12J25]
26E35 非标准分析 [另见 03H05、28E05、54J05]
26E40 构造实分析 [另见 03F60]
26E50 模糊实分析 [另见 03E72,28E10]
26E60 意味着 [另见 47A64]
26E70 时间尺度或测度链上的实分析{关于时间尺度或测度链上的动力学方程，参见34N05}
26E99 上述均非，但本节
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| 28-XX Measure and integration {For analysis on manifolds, see 58- XX} 28-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to measure and integration 28-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration 28-02 Research exposition (monographs, survey articles) pertaining to measure and integration 28-03 History of measure and integration [Consider also classification numbers pertaining to Section 01] 28-04 Software, source code, etc. for problems pertaining to measure and integration 28-06 Proceedings, conferences, collections, etc. pertaining to measure and integration 28-08 Computational methods for problems pertaining to measure and integration 28-11 Research data for problems pertaining to measure and integration |
28-XX 测量与集成{关于流形的分析，参见58-XX} 28-00 与测量和集成相关的通用参考文献（手册、词典、参考书目等）
28-01导论性阐述（教材、教程论文，等) 与测量和积分有关
28-02 研究性论文（专著、综述）：测量与整合相关
28-03 测量与积分的历史 [另请参阅第01节相关分类编号]
28-04 针对相关问题的软件、源代码等测积
28-06 会议记录、会议资料、文集等测积
28-08 与测度和积分相关问题的计算方法
28-11 测量与积分相关问题的研究数据
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| 28Axx Classical measure theory 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 28A10 Real- or complex-valued set functions 28A12 Contents, measures, outer measures, capacities 28A15 Abstract differentiation theory, differentiation of set functions [See also 26A24] 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 28A25 Integration with respect to measures and other set functions 28A33 Spaces of measures, convergence of measures [See also 46E27, 60Bxx] 28A35 Measures and integrals in product spaces 28A50 Integration and disintegration of measures 28A51 Lifting theory [See also 46G15] 28A60 Measures on Boolean rings, measure algebras [See also 54H10] 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] 28A78 Hausdorff and packing measures 28A80 Fractals [See also 37Fxx] 28A99 None of the above, but in this section |
28Axx 古典测度论 28A05 集合类（Borel域、 σ 环等）、可测集、Suslin集、解析集 [另见03E15、26A21、54H05] 28A10 实值或复值集合函数 28A12 内容、测度、外测度、容量 28A15 抽象微分理论与集合函数的微分 [另见26A24] 28A20 可测与不可测函数、可测函数序列、收敛方式 28A25 测度及其他集合函数的积分 28A33 测度空间、测度的收敛性 [另见46E27、60Bxx] 28A35 乘积空间中的测度与积分 28A50 测度的积分与分解 28A51 提升理论 [另见46G15] 28A60 布尔环上的测度、测度代数 [另见54H10] 28A75 长度、面积、体积及其他几何测度理论 [另见26B15、49Q15] 28A78 Hausdorff测度与堆积测度 28A80 分形 [另见37Fxx] 28A99 本节不涉及上述内容 |
| 28Bxx Set functions, measures and integrals with values in abstract spaces 28B05 Vector-valued set functions, measures and integrals [See also 46G10] 28B10 Group- or semigroup-valued set functions, measures and integrals 28B15 Set functions, measures and integrals with values in ordered spaces 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14] 28B99 None of the above, but in this section |
28Bxx 抽象空间值的集合函数、测度与积分 28B05 向量值集合函数、测度与积分 [另见 46G10] 28B10 群或半群值集合函数、测度与积分 28B15 有序空间值的集合函数、测度与积分 28B20 集值集合函数与测度；集值函数积分；可测选择 [另见 26E25、54C60、54C65、91B14] 28B99 本节不涉及上述内容 |
| 28Cxx Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20] 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures 28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures [See also 22Axx, 43A05] 28C15 Set functions and measures on topological spaces (regularity of measures, etc.) 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 28C99 None of the above, but in this section |
28Cxx 具有附加结构空间上的集合函数与测度[另见46G12、58C35、58D20] 28C05 通过线性泛函（如Radon测度、Daniell积分等）的积分理论，表示集合函数与测度 28C10 拓扑群或半群上的集合函数与测度、Haar测度、不变测度[另见22Axx、43A05] 28C15 拓扑空间上的集合函数与测度（测度的正则性等） 28C20 无限维空间中的集合函数与测度及积分（如Wiener测度、高斯测度等）[另见46G12、58C35、58D20、60B11] 28C99 本节不涉及上述内容 |
| 28Dxx Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 60Fxx, 60G10] 28D05 Measure-preserving transformations {For measure-preserving transformations and dynamical systems, see 37A05} 28D10 One-parameter continuous families of measurepreserving transformations {For dynamical systems aspect, see 37A10} 28D15 General groups of measure-preserving transformations {For dynamical systems aspects, see 37A15} 28D20 Entropy and other invariants 28D99 None of the above, but in this section |
28Dxx 测度论遍历理论 [另见 11K50、11K55、22D40、37Axx、47A35、60Fxx、60G10] 28D05 测度保持变换 {关于测度保持变换与动力系统，参见37A05}
28D10 一参数连续测度保持变换族{关于动力系统方面，参见37A10}
28D15 保持测度的变换的一般群 {关于动力系统方面的内容，参见37A15} 28D20 熵及其他不变量
28D99 本节不涉及上述内容
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| 28Exx Miscellaneous topics in measure theory 28E05 Nonstandard measure theory [See also 03H05, 26E35] 28E10 Fuzzy measure theory [See also 03E72, 26E50, 94D05] 28E15 Other connections with logic and set theory 28E99 None of the above, but in this section |
28Exx 测度论中的杂项问题 28E05 非标准测度论 [另见 03H05,26E35]
28E10 模糊测度理论 [另见 03E72、26E50、94D05]
28E15 其他与逻辑和集合论的联系
28E99 本节不涉及上述内容
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| 30-XX Functions of a complex variable 30-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable 30-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable 30-02 Research exposition (monographs, survey articles) pertaining to functions of a complex variable 30-03 History of functions of a complex variable [Consider also classification numbers pertaining to Section 01] 30-04 Software, source code, etc. for problems pertaining to functions of a complex variable 30-06 Proceedings, conferences, collections, etc. pertaining to functions of a complex variable 30-08 Computational methods for problems pertaining to functions of a complex variable [See also 65Exx] 30-11 Research data for problems pertaining to functions of a complex variable |
30-XX 复变函数 30-00 与复变量函数相关的通用参考文献（手册、词典、参考书目等）
30-01 复变函数相关导论性阐述（教材、辅导论文等）
30-02 关于复变量函数的研究文献（专著、综述文章）
30-03 复变函数研究进展史 [另请参阅第01节分类编号]
30-04 复变函数相关问题的软件、源代码等资料 30-06 复变函数相关会议论文集、学术汇编等文献 30-08 复变函数问题的计算方法研究 [另见65Exx] 30-11 复变函数相关问题的研究数据 |
| 30Axx General properties of functions of one complex variable 30A05 Monogenic and polygenic functions of one complex variable 30A10 Inequalities in the complex plane 30A99 None of the above, but in this section |
30Axx 复变函数的一般性质 30A05 复变函数的单基因与多基因函数 30A10 复平面上的不等式 30A99 本节不涉及上述内容 |
| 30Bxx Series expansions of functions of one complex variable 30B10 Power series (including lacunary series) in one complex variable 30B20 Random power series in one complex variable 30B30 Boundary behavior of power series in one complex variable; over-convergence 30B40 Analytic continuation of functions of one complex variable 30B50 Dirichlet series, exponential series and other series in one complex variable [See also 11M41, 42- XX] 30B60 Completeness problems, closure of a system of functions of one complex variable 30B70 Continued fractions; complex-analytic aspects [See also 11A55, 40A15] 30B99 None of the above, but in this section |
30Bxx系列复变函数扩展 30B10单复变量幂级数（含空缺级数）30B20单复变量随机幂级数 30B30单复变量幂级数的边界行为与超收敛性 30B40单复变量函数的解析延拓 30B50单复变量的狄利克雷级数、指数级数及其他级数[另见11M41、42-XX] 30B60函数完备性问题与单复变量函数系的闭包 30B70连分数的复解析特性[另见11A55、40A15] 30B99本节不涉及上述内容 |
| 30Cxx Geometric function theory 30C10 Polynomials and rational functions of one complex variable 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10} 30C20 Conformal mappings of special domains 30C25 Covering theorems in conformal mapping theory 30C30 Schwarz-Christoffel-type mappings [See also 65E10] 30C35 General theory of conformal mappings 30C40 Kernel functions in one complex variable and applications 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 30C50 Coefficient problems for univalent and multivalent functions of one complex variable 30C55 General theory of univalent and multivalent functions of one complex variable 30C62 Quasiconformal mappings in the complex plane 30C65 Quasiconformal mappings in R n, other generalizations 30C70 Extremal problems for conformal and quasiconformal mappings, variational methods 30C75 Extremal problems for conformal and quasiconformal mappings, other methods 30C80 Maximum principle, Schwarz’s lemma, Lindel¨of principle, analogues and generalizations; subordination 30C85 Capacity and harmonic measure in the complex plane [See also 31A15] 30C99 None of the above, but in this section |
30Cxx 几何函数理论 |
| 30Dxx Entire and meromorphic functions of one complex variable, and related topics 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable [See also 34Mxx, 37Fxx, 39-XX] 30D10 Representations of entire functions of one complex variable by series and integrals 30D15 Special classes of entire functions of one complex variable and growth estimates 30D20 Entire functions of one complex variable, general theory 30D30 Meromorphic functions of one complex variable, general theory 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D40 Cluster sets, prime ends, boundary behavior 30D45 Normal functions of one complex variable, normal families 30D60 Quasi-analytic and other classes of functions of one complex variable 30D99 None of the above, but in this section |
30Dxx 复变函数与亚纯函数及其相关主题 30D05 复平面上的函数方程、单复变解析函数的迭代与复合[另见34Mxx、37Fxx、39-XX] 30D10 用级数与积分表示单复变全函数 30D15 单复变全函数的特殊类与增长估计 30D20 单复变全函数的通论 30D30 单复变亚纯函数的通论 30D35 单复变亚纯函数的值分布与Nevanlinna理论 30D40 集群集、原端与边界行为 30D45 单复变正规函数与正规族 30D60 单复变拟解析函数及其他函数类 30D99 本节不涉及上述内容 |
| 30Exx Miscellaneous topics of analysis in the complex plane 30E05 Moment problems and interpolation problems in the complex plane 30E10 Approximation in the complex plane 30E15 Asymptotic representations in the complex plane 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane [See also 45Exx] 30E25 Boundary value problems in the complex plane [See also 45Exx] 30E99 None of the above, but in this section |
30Exx 复平面上的其他分析主题 30E05 复平面上的矩问题与插值问题 30E10 复平面上的逼近方法 30E15 复平面上的渐近表示 30E20 积分、柯西型积分、复平面上解析函数的积分表示 [另见 45Exx] 30E25 复平面上的边值问题 [另见 45Exx] 30E99 本节不涉及上述内容 |
| 30Fxx Riemann surfaces 30F10 Compact Riemann surfaces and uniformization [See also 14H15, 32G15] 30F15 Harmonic functions on Riemann surfaces 30F20 Classification theory of Riemann surfaces 30F25 Ideal boundary theory for Riemann surfaces 30F30 Differentials on Riemann surfaces 30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx] 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization) [See also 20H10] 30F45 Conformal metrics (hyperbolic, Poincar´e, distance functions) 30F50 Klein surfaces 30F60 Teichmu¨ller theory for Riemann surfaces [See also 32G15] 30F99 None of the above, but in this section |
30Fxx 莱曼曲面 30F10 紧致莱曼曲面与一致化 [另见 14H15,32G15] 30F15 莱曼曲面上的调和函数 30F20 莱曼曲面分类理论 30F25 莱曼曲面的理想边界理论 30F30 莱曼曲面上的微分 30F35 富克斯群与自守函数（紧致莱曼曲面与一致化的相关方面）[另见 11Fxx，20H10,22E40,32Gxx，32Nxx] 30F40 克莱因群（紧致莱曼曲面与一致化的相关方面）[另见 20H10] 30F45 保角度量（双曲度量、庞加莱度量、距离函数）30F50 克莱因曲面 30F60 莱曼曲面的泰希米勒理论 [另见 32G15] 30F99 本节不涉及上述内容 |
| 30Gxx Generalized function theory 30G06 Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05] 30G12 Finely holomorphic functions and topological function theory 30G20 Generalizations of Bers and Vekua type (pseudoanalytic, p-analytic, etc.) 30G25 Discrete analytic functions 30G30 Other generalizations of analytic functions (including abstract-valued functions) 30G35 Functions of hypercomplex variables and generalized variables 30G99 None of the above, but in this section |
30Gxx 普适函数论 30G06 非阿基米德函数论 [另见 12J25]；非标准函数论 [另见 03H05] 30G12 精细全纯函数与拓扑函数论 30G20 贝尔斯型与维库阿型函数的推广（伪解析、p-解析等） 30G25 离散解析函数 30G30 其他解析函数的推广（含抽象值函数） 30G35 超复变量与广义变量函数 30G99 本节不涉及上述内容 |
| 30Hxx Spaces and algebras of analytic functions of one complex variable 30H05 Spaces of bounded analytic functions of one complex variable 30H10 Hardy spaces [See also 42B30, 46E30] 30H15 Nevanlinna spaces and Smirnov spaces 30H20 Bergman spaces and Fock spaces [See also 46E30, 46E35] 30H25 Besov spaces and Qp-spaces 30H30 Bloch spaces 30H35 BMO-spaces 30H40 Zygmund spaces 30H45 de Branges-Rovnyak spaces 30H50 Algebras of analytic functions of one complex variable 30H80 Corona theorems 30H99 None of the above, but in this section |
30Hxx 复变函数解析空间与代数 30H05 复变函数有界解析空间 30H10 哈代空间 [另见 42B30,46E30] 30H15 内万林纳空间与斯米尔诺夫空间 30H20 贝格曼空间与福克空间 [另见 46E30,46E35] 30H25 贝索夫空间与Qp空间 30H30 布洛赫空间 30H35 BMO空间 30H40 西格蒙德空间 30H45 德布朗热-罗夫尼亚克空间 30H50 复变函数解析代数 30H80 冠定理 30H99 本节不涉及上述内容 |
| 30Jxx Function theory on the disc 30J05 Inner functions of one complex variable 30J10 Blaschke products 30J15 Singular inner functions of one complex variable 30J99 None of the above, but in this section |
30Jxx 离散函数论 30J05 复变函数内函数 30J10 布拉斯克积 30J15 复变函数奇异内函数 30J99 本节不涉及上述内容 |
| 30Kxx Universal holomorphic functions of one complex variable 30K05 Universal Taylor series in one complex variable 30K10 Universal Dirichlet series in one complex variable 30K15 Universal functions of one complex variable 30K20 Compositional universality 30K99 None of the above, but in this section |
30Kxx 复变函数全纯函数 30K05 复变函数泰勒级数 30K10 复变函数狄利克雷级数 30K15 复变函数泛函 30K20 复变函数复合泛函 30K99 本节不涉及上述内容 |
| 30Lxx Analysis on metric spaces 30L05 Geometric embeddings of metric spaces 30L10 Quasiconformal mappings in metric spaces 30L15 Inequalities in metric spaces 30L99 None of the above, but in this section |
30Lxx 度量空间分析 30L05 度量空间的几何嵌入 30L10 度量空间中的拟共形映射 30L15 度量空间中的不等式 30L99 本节不涉及上述内容 |
| 31-XX Potential theory {For probabilistic potential theory, see 60J45} 31-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to potential theory 31-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to potential theory 31-02 Research exposition (monographs, survey articles) pertaining to potential theory 31-03 History of potential theory [Consider also classification numbers pertaining to Section 01] 31-04 Software, source code, etc. for problems pertaining to potential theory 31-06 Proceedings, conferences, collections, etc. pertaining to potential theory 31-08 Computational methods for problems pertaining to potential theory [See also 65Exx] 31-11 Research data for problems pertaining to potential theory |
31-XX 势理论 {关于概率势理论，参见60J45} 31-00 与势理论相关的通用参考文献（手册、词典、参考书目等） 31-01 与势理论相关的入门性论述（教科书、教程论文等） 31-02 与势理论相关的研究性论述（专著、综述文章等） 31-03 势理论发展史 [另请参考第01章节的分类号] 31-04 与势理论相关问题的软件、源代码等 31-06 与势理论相关的会议论文集、学术汇编等 31-08 与势理论相关问题的计算方法 [另见65Exx] 31-11 与势理论相关问题的研究数据 |
| 31Axx Two-dimensional potential theory 31A05 Harmonic, subharmonic, superharmonic functions in two dimensions 31A10 Integral representations, integral operators, integral equations methods in two dimensions 31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions [See also 30C85] 31A20 Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions 31A25 Boundary value and inverse problems for harmonic functions in two dimensions 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions 31A35 Connections of harmonic functions with differential equations in two dimensions 31A99 None of the above, but in this section |
31Axx 二维势理论 31A05 二维空间中的调和函数、次调和函数与超调和函数 31A10 二维空间中的积分表示、积分算子与积分方程方法 31A15 二维空间中的势函数与容量、调和测度、极值长度及相关概念[另见30C85] 31A20 二维空间中调和函数的边界行为（法图型定理等）31A25 二维空间中调和函数的边值问题与反问题 31A30 二维空间中的双调和函数、多调和函数与方程、泊松方程 31A35 二维空间中调和函数与微分方程的联系 31A99 本节不涉及上述内容 |
| 31Bxx Higher-dimensional potential theory 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions 31B10 Integral representations, integral operators, integral equations methods in higher dimensions 31B15 Potentials and capacities, extremal length and related notions in higher dimensions 31B20 Boundary value and inverse problems for harmonic functions in higher dimensions 31B25 Boundary behavior of harmonic functions in higher dimensions 31B30 Biharmonic and polyharmonic equations and functions in higher dimensions 31B35 Connections of harmonic functions with differential equations in higher dimensions 31B99 None of the above, but in this section |
31Bxx 高维势理论 31B05 高维空间中的调和函数、次调和函数与超调和函数 31B10 高维空间中的积分表示、积分算子与积分方程方法 31B15 高维空间中的势函数与容量、极值长度及相关概念 31B20 高维空间中调和函数的边值问题与反问题 31B25 高维空间中调和函数的边界行为 31B30 高维空间中的双调和方程与多调和方程及函数 31B35 高维空间中调和函数与微分方程的联系 31B99 本节不涉及上述内容 |
| 31Cxx Generalizations of potential theory 31C05 Harmonic, subharmonic, superharmonic functions on other spaces 31C10 Pluriharmonic and plurisubharmonic functions [See also 32U05] 31C12 Potential theory on Riemannian manifolds and other spaces [See also 53C20] {For Hodge theory, see 58A14} 31C15 Potentials and capacities on other spaces 31C20 Discrete potential theory 31C25 Dirichlet forms 31C35 Martin boundary theory [See also 60J50] 31C40 Fine potential theory; fine properties of sets and functions 31C45 Other generalizations (nonlinear potential theory, etc.) 31C99 None of the above, but in this section |
31Cxx 势理论的推广 31C05 其他空间上的调和函数、次调和函数与超调和函数 31C10 多调和函数与多次调和函数 [另见 32U05] 31C12 兰曼流形及其他空间上的势理论 [另见 53C20] {关于霍奇理论，参见 58A14} 31C15 其他空间上的势与容量 31C20 离散势理论 31C25 迪里克雷形式 31C35 马丁边界理论 [另见 60J50] 31C40 精细势理论；集合与函数的精细性质 31C45 其他推广（非线性势理论等） 31C99 本节不涉及上述内容 |
| 31Dxx Axiomatic potential theory 31D05 Axiomatic potential theory 31D99 None of the above, but in this section |
31Dxx 原理性潜能理论 31D05 原理性潜能理论
31D99 本节不涉及上述内容
|
| 31Exx Potential theory on fractals and metric spaces 31E05 Potential theory on fractals and metric spaces 31E99 None of the above, but in this section |
31Exx 分形与度量空间的势理论 31E05 分形与度量空间的势理论
31E99 本节不涉及上述内容
|
| 32-XX Several complex variables and analytic spaces {For infinitedimensional holomorphy, see also 46G20, 58B12} 32-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces 32-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces 32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces 32-03 History of several complex variables and analytic spaces [Consider also classification numbers pertaining to Section 01] 32-04 Software, source code, etc. for problems pertaining to several complex variables and analytic spaces 32-06 Proceedings, conferences, collections, etc. pertaining to several complex variables and analytic spaces 32-08 Computational methods for problems pertaining to several complex variables and analytic spaces [See also 65Exx] 32-11 Research data for problems pertaining to several complex variables and analytic spaces |
32-XX 多个复变量与解析空间 {关于无限维全纯性，另见46G20、58B12} 32-00 关于多个复杂变量与分析空间的通用参考文献（手册、词典、参考书目等）
32-01 与复变量及解析空间相关的导论性阐述（教材、辅导论文等）
32-02 关于多个复杂变量与分析空间的研究文献（专著、综述文章）
32-03 复变数与解析空间的历史 [另参见第01节相关分类编号]
32-04 软件、源代码等，用于解决涉及多个复杂变量和解析空间的问题
32-06 与多个复变量及解析空间相关的会议记录、会议论文集等
32-08 多复变量与解析空间相关问题的计算方法 [另见 65Exx]
32-11 多个复杂变量与解析空间相关问题的研究数据
|
| 32Axx Holomorphic functions of several complex variables 32A05 Power series, series of functions of several complex variables 32A08 Polynomials and rational functions of several complex variables 32A10 Holomorphic functions of several complex variables 32A12 Multifunctions of several complex variables 32A15 Entire functions of several complex variables 32A17 Special families of functions of several complex variables 32A18 Bloch functions, normal functions of several complex variables 32A19 Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.) 32A20 Meromorphic functions of several complex variables 32A22 Nevanlinna theory; growth estimates; other inequalities of several complex variables {For geometric theory, see 32H25, 32H30} 32A25 Integral representations; canonical kernels (Szeg˝o, Bergman, etc.) 32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappi`e-type kernels) 32A27 Residues for several complex variables [See also 32C30] 32A30 Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35} 32A35 Hp -spaces, Nevanlinna spaces of functions in several complex variables [See also 32M15, 42B30, 43A85, 46J15] 32A36 Bergman spaces of functions in several complex variables 32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 32A38 Algebras of holomorphic functions of several complex variables [See also 46J10, 46J15] 32A40 Boundary behavior of holomorphic functions of several complex variables 32A45 Hyperfunctions [See also 46F15] 32A50 Harmonic analysis of several complex variables [See mainly 43-XX] 32A55 Singular integrals of functions in several complex variables 32A60 Zero sets of holomorphic functions of several complex variables 32A65 Banach algebra techniques applied to functions of several complex variables [See also 46Jxx] 32A70 Functional analysis techniques applied to functions of several complex variables [See also 46Exx] 32A99 None of the above, but in this section |
32Axx 多元全纯函数复变量 32A05 功率级数，复数级数函数可变因素 |
| 32Bxx Local analytic geometry [See also 13-XX, 14-XX] 32B05 Analytic algebras and generalizations, preparation theorems 32B10 Germs of analytic sets, local parametrization 32B15 Analytic subsets of affine space 32B20 Semi-analytic sets, subanalytic sets, and generalizations [See also 14P15] 32B25 Triangulation and topological properties of semianalytic andsubanalytic sets, and related questions 32B99 None of the above, but in this section |
32Bxx 局部解析几何 [另见13-XX, 14-XX] 32B05 分析代数与推广，预备课程定理
32B10 分析集的芽，局部参数化
32B15仿射空间的解析子集
32B20 半解析集、子解析集与推广[另见14P15]
32B25 三边测量与半解析的拓扑性质以及次解析集及相关问题
32B99 本节不涉及上述内容 |
| 32Cxx Analytic spaces 32C05 Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07] 32C07 Real-analytic sets, complex Nash functions [See also 14P15, 14P20] 32C09 Embedding of real-analytic manifolds 32C11 Complex supergeometry [See also 14A22, 14M30, 58A50] 32C15 Complex spaces 32C18 Topology of analytic spaces 32C20 Normal analytic spaces 32C22 Embedding of analytic spaces 32C25 Analytic subsets and submanifolds 32C30 Integration on analytic sets and spaces, currents [See also 32A25, 32A27] 32C35 Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30] 32C36 Local cohomology of analytic spaces 32C37 Duality theorems for analytic spaces 32C38 Sheaves of differential operators and their modules, D-modules [See also 14F10, 16S32, 35A27, 58J15] 32C55 The Levi problem in complex spaces; generalizations 32C81 Applications of analytic spaces to physics and other areas of science 32C99 None of the above, but in this section |
32Cxx 分析空间 32C05 实解析流形与实解析空间 [另见 14Pxx、58A07] 32C07 实解析集与复纳什函数 [另见 14P15、14P20] 32C09 实解析流形的嵌入 32C11 复超几何 [另见 14A22、14M30、58A50] 32C15 复空间 32C18 分析空间的拓扑学 32C20 正则解析空间 32C22 分析空间的嵌入 32C25 分析子集与子流形 32C30 分析集与空间上的积分、流 [另见 32A25、32A27] 32C35 分析层与上同调群 [另见 14Fxx、18F20、55N30] 32C36 分析空间的局部上同调 32C37 分析空间的对偶定理 32C38 微分算子层及其模、D-模 [另见 14F10、16S32、35A27、58J15] 32C55 复空间中的Levi问题及其推广 32C81 分析空间在物理学及其他科学领域的应用 32C99 本节不涉及上述内容 |
| 32Dxx Analytic continuation 32D05 Domains of holomorphy 32D10 Envelopes of holomorphy 32D15 Continuation of analytic objects in several complex variables 32D20 Removable singularities in several complex variables 32D26 Riemann domains 32D99 None of the above, but in this section |
32Dxx 分析延拓 32D05 全纯性域 32D10 全纯性包络 32D15 复变函数解析对象的延拓 32D20 复变函数可去奇异点 32D26 黎曼域 32D99 本节不涉及上述内容 |
| 32Exx Holomorphic convexity 32E05 Holomorphically convex complex spaces, reduction theory 32E10 Stein spaces, Stein manifolds 32E20 Polynomial convexity, rational convexity, meromorphic convexity in several complex variables 32E30 Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs 32E35 Global boundary behavior of holomorphic functions of several complex variables 32E40 The Levi problem 32E99 None of the above, but in this section |
32Exx 全纯凸性 32E05 全纯凸复空间的约化理论
32E10 斯坦空间，斯坦流形
32E20 多复变量中的多项式凸性、有理凸性与亚纯凸性 32E30 多复变量中的全纯函数、多项式与有理函数逼近及插值；Runge配对
32E35 多复变量全纯函数的全局边界行为 32E40 Levi问题 32E99 本节不涉及上述内容 |
| 32Fxx Geometric convexity in several complex variables 32F10 q-convexity, q-concavity 32F17 Other notions of convexity in relation to several complex variables 32F18 Finite-type conditions for the boundary of a domain 32F27 Topological consequences of geometric convexity 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.) 32F45 Invariant metrics and pseudodistances in several complex variables 32F99 None of the above, but in this section |
32Fxx 复变函数中的几何凸性 32F10 q-凸性与q-凹性 32F17 复变函数中其他凸性概念 32F18 域边界的有限型条件 32F27 几何凸性的拓扑性质 32F32 几何凸性的解析性质（消失定理等） 32F45 复变函数中的不变度量与伪距离 32F99 本节不涉及上述内容 |
| 32Gxx Deformations of analytic structures 32G05 Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15] 32G07 Deformations of special (e.g., CR) structures 32G08 Deformations of fiber bundles 32G10 Deformations of submanifolds and subspaces 32G13 Complex-analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15] 32G15 Moduli of Riemann surfaces, Teichmu¨ller theory (complex-analytic aspects in several variables) [See also 14H15, 30Fxx] 32G20 Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30] 32G34 Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) [See also 34Mxx] 32G81 Applications of deformations of analytic structures to the sciences 32G99 None of the above, but in this section |
32Gxx 分析结构的形变
32G05 复结构的形变 [另见 13D10、16S80、58H10、58H15] |
| 32Hxx Holomorphic mappings and correspondences 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables 32H04 Meromorphic mappings in several complex variables 32H12 Boundary uniqueness of mappings in several complex variables 32H25 Picard-type theorems and generalizations for several complex variables {For function-theoretic properties, see 32A22} 32H30 Value distribution theory in higher dimensions {For function-theoretic properties, see 32A22} 32H35 Proper holomorphic mappings, finiteness theorems 32H40 Boundary regularity of mappings in several complex variables 32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables 32H99 None of the above, but in this section |
32Hxx 全纯映射与对应关系 32H02 复变函数中的全纯映射、（全纯）嵌入及相关问题 32H04 复变函数中的亚全纯映射 32H12 复变函数映射的边界唯一性 32H25 复变函数的皮卡型定理及其推广（函数论性质参见32A22） 32H30 高维值分布理论（函数论性质参见32A22） 32H35 真全纯映射与有限性定理 32H40 复变函数映射的边界正则性 32H50 复变函数全纯映射的迭代、不动点及相关问题 32H99 本节不涉及上述内容 |
| 32Jxx Compact analytic spaces {For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx} 32J05 Compactification of analytic spaces 32J10 Algebraic dependence theorems 32J15 Compact complex surfaces 32J17 Compact complex 3-folds 32J18 Compact complex n-folds 32J25 Transcendental methods of algebraic geometry (complex-analytic aspects) [See also 14C30] 32J27 Compact K¨ahler manifolds: generalizations, classification 32J81 Applications of compact analytic spaces to the sciences 32J99 None of the above, but in this section |
32Jxx 紧致解析空间 {关于黎曼曲面的理论，参见14Hxx、30Fxx；代数理论相关内容，参见14Jxx} |
| 32Kxx Generalizations of analytic spaces 32K05 Banach analytic manifolds and spaces [See also 46G20, 58Bxx] 32K07 Formal and graded complex spaces [See also 58C50] 32K12 Holomorphic maps with infinite-dimensional arguments or values [See also 46G20] 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also 58C25] 32K99 None of the above, but in this section 32Lxx Holomorphic fiber spaces [See also 55Rxx] 32L05 Holomorphic bundles and generalizations 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F06, 14H60, 14J60, 18F20, 55N30] 32L15 Bundle convexity [See also 32F10] 32L20 Vanishing theorems 32L25 Twistor theory, double fibrations (complexanalytic aspects) [See also 53C28] 32L81 Applications of holomorphic fiber spaces to the sciences 32L99 None of the above, but in this section |
32Kxx 解析空间的推广 32K05 Banach解析流形与空间 [另见46G20、58Bxx]
32K07 形式化与分级复空间 [另见58C50] 32K12 无限维参数或值的全纯映射 [另见46G20] 32K15 分析空间与可微空间上的可微函数 [另见58C25] 32K99 上述均非，但本节32Lxx 全纯纤维空间 [另见55Rxx] 32L05 全纯丛及其推广 32L10 全纯向量丛层与截面上同调的普遍结果 [另见14F06、14H60、14J60、18F20、55N30] 32L15 丛凸性 [另见32F10] 32L20 消失定理 32L25 扭量理论与双纤维化（复解析方面）[另见53C28] 32L81 全纯纤维空间在科学中的应用 32L99 本节不涉及上述内容 |
| 32Mxx Complex spaces with a group of automorphisms 32M05 Complex Lie groups, group actions on complex spaces [See also 22E10] 32M10 Homogeneous complex manifolds [See also 14M17, 57T15] 32M12 Almost homogeneous manifolds and spaces [See also 14M17] 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) [See also 22E10, 22E40, 53C35, 57T15] 32M17 Automorphism groups of C n and affine manifolds 32M18 Automorphism groups of other complex spaces 32M25 Complex vector fields, holomorphic foliations, Cactions 32M99 None of the above, but in this section |
32Mxx 具有自同构群的复空间 32M05 复Lie群，群在复空间上的作用 [另见22E10]
32M10 同质复流形 [另见 14M17,57T15]
32M12 几乎齐性流形与空间 [另见 14M17]
32M15 赫米特对称空间、有界对称域、若尔当代数（复解析特性）[另见 22E10、22E40、53C35、57T15]
32M17 C n的自同构群与仿射流形
32M18 其他复空间的自同构群
32M25 复向量场、全纯叶状结构、C作用
32M99 本节不涉及上述内容
|
| 32Nxx Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35] 32N05 General theory of automorphic functions of several complex variables 32N10 Automorphic forms in several complex variables 32N15 Automorphic functions in symmetric domains 32N99 None of the above, but in this section |
32Nxx 自守函数 [另见 11Fxx、20H10、22E40、30F35] 32N05 多复变量自守函数通论 32N10 多复变量自守形式 32N15 对称域中的自守函数 32N99 本节不涉及上述内容 |
| 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) 32P05 Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) 32P99 None of the above, but in this section |
32Pxx 非阿基米德分析（还应分配至少一个来自第32节的其他分类编号，该章节描述了问题类型） 32P05 非阿基米德分析（还应分配至少一个来自第32节的其他分类编号，该章节描述了问题类型） 32P99 本节不涉及上述内容 |
| 32Qxx Complex manifolds 32Q02 Special domains (Reinhardt, Hartogs, circular, tube, etc.) in C n and complex manifolds 32Q05 Negative curvature complex manifolds 32Q10 Positive curvature complex manifolds 32Q15 K¨ahler manifolds 32Q20 K¨ahler-Einstein manifolds [See also 53Cxx] 32Q25 Calabi-Yau theory (complex-analytic aspects) [See also 14J32] 32Q26 Notions of stability for complex manifolds 32Q28 Stein manifolds 32Q30 Uniformization of complex manifolds 32Q35 Complex manifolds as subdomains of Euclidean space 32Q40 Embedding theorems for complex manifolds 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds 32Q55 Topological aspects of complex manifolds 32Q56 Oka principle and Oka manifolds 32Q57 Classification theorems for complex manifolds 32Q60 Almost complex manifolds 32Q65 Pseudoholomorphic curves 32Q99 None of the above, but in this section |
32Qxx 复流形 32Q02 特殊结构域（Reinhardt、Hartogs、环状结构）导管等)在C中n维复流形
32Q05 负曲率复流形
32Q10 正曲率复流形
32Q15凯勒流形
32Q20 卡勒-爱因斯坦流形 [另见 53Cxx]
32Q25 Calabi-Yau理论（复分析方面）[另见14J32]
32Q26 复流形的稳定性概念
32Q28 斯坦流形
32Q30 复流形的统一化
32Q35 复流形作为欧氏空间的子域空间复流形的32Q40嵌入定理
32Q45双曲流形和小林双曲流形
32Q55 复流形的拓扑性质 32Q56 Oka原理与Oka流形复流形的
32Q57分类定理 32Q60 几乎复流形
32Q65 假全纯曲线
32Q99 本节不涉及上述内容
|
| 32Sxx Complex singularities [See also 58Kxx] 32S05 Local complex singularities [See also 14J17] 32S10 Invariants of analytic local rings 32S15 Equisingularity (topological and analytic) [See also 14E15] 32S20 Global theory of complex singularities; cohomological properties [See also 14E15] 32S22 Relations with arrangements of hyperplanes [See also 52C35] 32S25 Complex surface and hypersurface singularities [See also 14J17] 32S30 Deformations of complex singularities; vanishing cycles [See also 14B07] 32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects) [See also 14C30, 14D07] 32S40 Monodromy; relations with differential equations and D-modules (complex-analytic aspects) 32S45 Modifications; resolution of singularities (complex-analytic aspects) [See also 14E15] 32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants 32S55 Milnor fibration; relations with knot theory [See also 57K10, 57K45] 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) [See also 58Kxx] 32S65 Singularities of holomorphic vector fields and foliations 32S70 Other operations on complex singularities 32S99 None of the above, but in this section |
32Sxx 复变奇点 [另见58Kxx] 32S05 局部复数奇点 [另见 14J17]
32S10解析局部环的不变量 32S15 等奇异（拓扑与解析）[另见 14E15]
32S20 复变奇点的全局理论；上同调特性 [另见14E15]
32S22 与超平面排列的关系[另见52C35]
32S25 复面与超曲面奇点[另见14J17]
32S30 复变奇点的形变；消失周期 [另见 14B07]
32S35奇异簇的混合Hodge理论（复解析方面）[另见14C30、14D07]
32S40单值性；与微分方程及D-模的关系（复解析方面） 32S45 修正；奇点解析（复分析方面）[另见14E15]
32S50 复变奇点的拓扑学特性：Lef-schetz定理，拓扑分类，不变量
32S55 米尔诺纤维化；与纽结理论的关系[另见57K10,57K45]
32S60 分层；可构造层；交上同调（复分析方面）[另见58Kxx]
32S65全纯向量场与叶状结构的奇点
32S70 复奇点的其他运算
32S99 本节不涉及上述内容
|
| 32Txx Pseudoconvex domains 32T05 Domains of holomorphy 32T15 Strongly pseudoconvex domains 32T20 Worm domains 32T25 Finite-type domains 32T27 Geometric and analytic invariants on weakly pseudoconvex boundaries 32T35 Exhaustion functions 32T40 Peak functions 32T99 None of the above, but in this section |
32Txx 伪凸域 32T05 全纯域 32T15 强伪凸域 32T20 蠕虫域 32T25 有限型域 32T27 弱伪凸边界上的几何与解析不变量 32T35 消耗函数 32T40 峰函数 32T99 本节不涉及上述内容 |
| 32Uxx Pluripotential theory 32U05 Plurisubharmonic functions and generalizations [See also 31C10] 32U10 Plurisubharmonic exhaustion functions 32U15 General pluripotential theory 32U20 Capacity theory and generalizations 32U25 Lelong numbers 32U30 Removable sets in pluripotential theory 32U35 Plurisubharmonic extremal functions, pluricomplex Green functions 32U40 Currents 32U99 None of the above, but in this section |
32Uxx 多潜能理论 32U05 多次调和函数及其推广[另见31C10] 32U10 多次调和耗竭函数 32U15 一般多潜能理论 32U20 容量理论及其推广 32U25 莱隆数 32U30 多潜能理论中的可去集 32U35 多次调和极值函数与复格林函数 32U40 电流 32U99 本节不涉及上述内容 |
| 32Vxx CR manifolds 32V05 CR structures, CR operators, and generalizations 32V10 CR functions 32V15 CR manifolds as boundaries of domains 32V20 Analysis on CR manifolds 32V25 Extension of functions and other analytic objects from CR manifolds 32V30 Embeddings of CR manifolds 32V35 Finite-type conditions on CR manifolds 32V40 Real submanifolds in complex manifolds 32V99 None of the above, but in this section |
32Vxx CR流形 32V05 CR结构、CR算子及其推广 32V10 CR函数 32V15 作为域边界的CR流形 32V20 CR流形分析 32V25 函数及其他解析对象在CR流形上的延拓 32V30 CR流形的嵌入 32V35 CR流形的有限型条件 32V40 复流形中的实子流形 32V99 本节不涉及上述内容 |
| 32Wxx Differential operators in several variables 32W05 ∂ and ∂-Neumann operators 32W10 ∂b and ∂b-Neumann operators 32W20 Complex Monge-Amp`ere operators 32W25 Pseudodifferential operators in several complex variables 32W30 Heat kernels in several complex variables 32W50 Other partial differential equations of complex analysis in several variables 32W99 None of the above, but in this section |
32Wxx 多变量微分算子 32W05 ∂和∂-诺伊曼算子 32W10 ∂b和∂b-诺伊曼算子 32W20 复变蒙日-安培算子 32W25 多复变量伪微分算子 32W30 多复变量热核 32W50 其他多变量复变分析偏微分方程 32W99 本节不涉及上述内容 |
| 33-XX Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics, see 05Axx; for number-theoretic aspects, see 11- XX; for representation theory, see 22Exx} 33-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions 33-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions 33-02 Research exposition (monographs, survey articles) pertaining to special functions 33-03 History of special functions [Consider also classification numbers pertaining to Section 01] 33-04 Software, source code, etc. for problems pertaining to special functions 33-06 Proceedings, conferences, collections, etc. pertaining to special functions 33-11 Research data for problems pertaining to special functions |
33-XX 特殊函数（33-XX研究函数作为函数的性质）{正交函数参见42Cxx；组合学相关参见05Axx；数论相关参见11-XX；表示论相关参见22Exx} 33-00 与特殊函数相关的通用参考文献（手册、词典、参考书目等） 33-01 与特殊函数相关的入门性论述（教科书、教程论文等） 33-02 与特殊函数相关的研究性论述（专著、综述文章等） 33-03 特殊函数的历史沿革[另请参考第01节的分类编号] 33-04 与特殊函数相关问题的软件、源代码等资源 33-06 与特殊函数相关的会议论文集、学术汇编等 33-11 与特殊函数相关问题的研究数据 |
| 33Bxx Elementary classical functions 33B10 Exponential and trigonometric functions 33B15 Gamma, beta and polygamma functions 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) 33B30 Higher logarithm functions 33B99 None of the above, but in this section |
33Bxx 基础经典函数 33B10 指数与三角函数 33B15 γ、β及多γ函数 33B20 不完全β与γ函数（误差函数、概率积分、菲涅尔积分） 33B30 高阶对数函数 33B99 本节不涉及上述内容 |
| 33Cxx Hypergeometric functions 33C05 Classical hypergeometric functions, 2F1 33C10 Bessel and Airy functions, cylinder functions, 0F1 33C15 Confluent hypergeometric functions, Whittaker functions, 1F1 33C20 Generalized hypergeometric series, pFq 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) {For general orthogonal polynomials and functions, see also 42C05} 33C47 Other special orthogonal polynomials and functions 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable 33C52 Orthogonal polynomials and functions associated with root systems 33C55 Spherical harmonics 33C60 Hypergeometric integrals and functions defined by them (E, G, H and I functions) 33C65 Appell, Horn and Lauricella functions 33C67 Hypergeometric functions associated with root systems 33C70 Other hypergeometric functions and integrals in several variables 33C75 Elliptic integrals as hypergeometric functions 33C80 Connections of hypergeometric functions with groups and algebras, and related topics 33C90 Applications of hypergeometric functions 33C99 None of the above, but in this section |
33Cxx 超几何函数 33C05 经典超几何函数，2F1 33C10 贝塞尔函数与艾里函数、柱面函数，0F1 33C15 融合超几何函数、惠特克函数，1F1 33C20 广义超几何级数，pFq 33C45 正交多项式与超几何型函数（雅可比、拉盖尔、埃尔米特、阿斯基方案等）{关于一般正交多项式与函数，另见42C05} 33C47 其他特殊正交多项式与函数 33C50 可用单变量特殊函数表示的多变量正交多项式与函数 33C52 与根系相关的正交多项式与函数 33C55 球面调和函数 33C60 超几何积分及其定义的函数（E、G、H和I函数） 33C65 阿佩尔函数、霍恩函数与劳里切拉函数 33C67 与根系相关的超几何函数 33C70 多变量其他超几何函数与积分 33C75 椭圆积分作为超几何函数 33C80 超几何函数与群代数的联系及相关课题 33C90 超几何函数的应用 33C99 本节不涉及上述内容 |
| 33Dxx Basic hypergeometric functions 33D05 q-gamma functions, q-beta functions and integrals 33D15 Basic hypergeometric functions in one variable, rφs 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) 33D60 Basic hypergeometric integrals and functions defined by them 33D65 Bibasic functions and multiple bases 33D67 Basic hypergeometric functions associated with root systems 33D70 Other basic hypergeometric functions and integrals in several variables 33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and related topics 33D90 Applications of basic hypergeometric functions 33D99 None of the above, but in this section |
33Dxx 基本超几何函数 33D05 q-伽马函数、q-贝塔函数及积分 33D15 一元基本超几何函数与 rφs 33D45 基本正交多项式与函数（如Askey-Wilson多项式等） 33D50 可用一元基本超几何函数表示的多变量正交多项式与函数 33D52 与根系相关的基正交多项式及函数（如Macdonald多项式等） 33D60 基本超几何积分及其定义的函数 33D65 双基函数与多重基 33D67 与根系相关的基本超几何函数 33D70 多变量其他基本超几何函数与积分 33D80 基本超几何函数与量子群、Chevalley群、p进群、Hecke代数及相关主题的联系 33D90 基本超几何函数的应用 33D99 本节不涉及上述内容 |
| 33Exx Other special functions 33E05 Elliptic functions and integrals 33E10 Lam´e, Mathieu, and spheroidal wave functions 33E12 Mittag-Leffler functions and generalizations 33E15 Other wave functions 33E17 Painlev´e-type functions 33E20 Other functions defined by series and integrals 33E30 Other functions coming from differential, difference and integral equations 33E50 Special functions in characteristic p (gamma functions, etc.) 33E99 None of the above, but in this section |
33Exx 其他特殊函数 33E05 椭圆函数与积分 33E10 拉梅函数、马蒂厄函数及球面波函数 33E12 米塔格-莱夫勒函数及其推广形式 33E15 其他波函数 33E17 帕涅列夫型函数 33E20 由级数与积分定义的其他函数 33E30 源自微分方程、差分方程及积分方程的其他函数 33E50 特征参数p的特殊函数（如伽马函数等） 33E99 本节不涉及上述内容 |
| 33Fxx Computational aspects of special functions {For software etc., see 33-04} 33F05 Numerical approximation and evaluation of special functions [See also 65D20] 33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) [See also 68W30] 33F99 None of the above, but in this section |
33Fxx 特殊函数的计算方法（软件相关请参见33-04） 33F05 特殊函数的数值逼近与计算[另见65D20] 33F10 特殊函数的符号计算（戈斯珀算法、蔡尔伯格算法等）[另见68W30] 33F99 本节不涉及上述内容 |
| 34-XX Ordinary differential equations 34-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations 34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations 34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations 34-03 History of ordinary differential equations [Consider also classification numbers pertaining to Section 01] 34-04 Software, source code, etc. for problems pertaining to ordinary differential equations 34-06 Proceedings, conferences, collections, etc. pertaining to ordinary differential equations 34-11 Research data for problems pertaining to ordinary differential equations |
34-XX 常微分方程 34-00 常微分方程相关通用参考文献（手册、词典、书目等） 34-01 常微分方程入门教材（教科书、教程论文等） 34-02 常微分方程研究专著（专著、综述文章等） 34-03 常微分方程发展史[另见01章节分类号] 34-04 常微分方程相关问题的软件、源代码等 34-06 常微分方程相关会议论文集、学术汇编等 34-11 常微分方程相关问题的研究数据 |
| 34Axx General theory for ordinary differential equations 34A05 Explicit solutions, first integrals of ordinary differential equations 34A06 Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.) 34A07 Fuzzy ordinary differential equations 34A08 Fractional ordinary differential equations and fractional differential inclusions 34A09 Implicit ordinary differential equations, differential-algebraic equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. [See also 44-XX] 34A26 Geometric methods in ordinary differential equations 34A30 Linear ordinary differential equations and systems, general 34A33 Ordinary lattice differential equations 34A34 Nonlinear ordinary differential equations and systems, general theory 34A35 Ordinary differential equations of infinite order 34A36 Discontinuous ordinary differential equations 34A37 Ordinary differential equations with impulses 34A38 Hybrid systems of ordinary differential equations 34A40 Differential inequalities involving functions of a single real variable [See also 26D20] 34A45 Theoretical approximation of solutions to ordinary differential equations {For numerical analysis, see 65Lxx} 34A55 Inverse problems involving ordinary differential equations 34A60 Ordinary differential inclusions [See also 49J21, 49K21] 34A99 None of the above, but in this section |
34Axx 常微分方程通论 34A05 常微分方程显式解与初等积分 34A06 广义常微分方程（测度微分方程、集合值微分方程等） 34A07 模糊微分方程 34A08 分式微分方程与分式微分包含关系 34A09 隐微分方程与微分代数方程 34A12 常微分方程初值问题：解的存在性、唯一性、连续依赖性与延拓性 34A25 常微分方程解析理论：级数、变换、运算、算子等[另见44-XX] 34A26 常微分方程几何方法 34A30 线性常微分方程与系统（通论） 34A33 常格微分方程 34A34 非线性常微分方程与系统（通论） 34A35 无限阶常微分方程 34A36 不连续常微分方程 34A37 带冲量的常微分方程 34A38 常微分方程混合系统 34A40 单变量函数微分不等式[另见26D20] 34A45 常微分方程解的理论逼近{数值分析参见65Lxx} 34A55 常微分方程逆问题 34A60 常微分包含关系[另见49J21]49K21] 34A99 本节不涉及上述内容 |
| 34Bxx Boundary value problems for ordinary differential equations {For ordinary differential operators, see 34Lxx} 34B05 Linear boundary value problems for ordinary differential equations 34B07 Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter 34B08 Parameter dependent boundary value problems for ordinary differential equations 34B09 Boundary eigenvalue problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B16 Singular nonlinear boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B20 Weyl theory and its generalizations for ordinary differential equations 34B24 Sturm-Liouville theory [See also 34Lxx] 34B27 Green’s functions for ordinary differential equations 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 34B37 Boundary value problems with impulses for ordinary differential equations 34B40 Boundary value problems on infinite intervals for ordinary differential equations 34B45 Boundary value problems on graphs and networks for ordinary differential equations 34B60 Applications of boundary value problems involving ordinary differential equations 34B99 None of the above, but in this section |
34Bxx 常微分方程的边界值问题 {关于常微分算子的讨论，请参见34Lxx} 34B05 常微分方程的线性边界值问题 34B07 光谱参数非线性依赖的常微分方程线性边界值问题 34B08 常微分方程的参数依赖边界值问题 34B09 常微分方程的边界特征值问题 34B10 常微分方程的非局部与多点边界值问题 34B15 常微分方程的非线性边界值问题 34B16 常微分方程的奇异非线性边界值问题 34B18 常微分方程非线性边界值问题的正解 34B20 常微分方程的Weyl理论及其推广 34B24 Sturm-Liouville理论 [另见34Lxx] 34B27 常微分方程的格林函数 34B30 特殊常微分方程（马蒂厄、希尔、贝塞尔等） 34B37 常微分方程的脉冲边界值问题 34B40 常微分方程的无限区间边界值问题 34B45 常微分方程的图与网络边界值问题 34B60 常微分方程边界值问题的应用 34B99 本节不涉及上述内容 |
| 34Cxx Qualitative theory for ordinary differential equations [See also 37-XX] 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations 34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 34C12 Monotone systems involving ordinary differential equations 34C14 Symmetries, invariants of ordinary differential equations [See also 37C79] 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms 34C23 Bifurcation theory for ordinary differential equations [See also 37Gxx] 34C25 Periodic solutions to ordinary differential equations 34C26 Relaxation oscillations for ordinary differential equations 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations [See also 37Dxx] 34C29 Averaging method for ordinary differential equations 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 34C40 Ordinary differential equations and systems on manifolds 34C41 Equivalence and asymptotic equivalence of ordinary differential equations 34C45 Invariant manifolds for ordinary differential equations 34C46 Multifrequency systems of ordinary differential equations 34C55 Hysteresis for ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 34C99 None of the above, but in this section |
34Cxx 常微分方程定性理论 [另见37-XX] 34C05 积分曲线拓扑结构、奇点与常微分方程极限环 34C07 多项式及解析向量场极限环理论（存在性、唯一性、界值、希尔伯特第16问题及其分支）在常微分方程中的应用 34C08 常微分方程与实代数几何的联系（多项式、去奇异化、阿贝尔积分零点等） 34C10 常微分方程振荡理论、零点、解的非共轭性及比较理论 34C11 常微分方程解的增长与有界性 34C12 涉及常微分方程的单调系统 34C14 常微分方程的对称性与不变量 [另见37C79] 34C15 常微分方程的非线性振荡与耦合振子 34C20 常微分方程与系统的变换与约化 34C23 常微分方程的分岔理论[另见37Gxx] 34C25 常微分方程的周期解 34C26 常微分方程的弛豫振荡 34C27 常微分方程的近似周期与伪近似周期解 34C28 常微分方程的复杂行为与混沌系统[另见37Dxx] 34C29 常微分方程的平均化方法 34C37 常微分方程的同宿与异宿解 34C40 流形上的常微分方程与系统 34C41 常微分方程的等价性与渐近等价性 34C45 常微分方程的不变流形 34C46 常微分方程的多频系统 34C55 常微分方程的迟滞现象 34C60 常微分方程模型的定性研究与仿真 34C99 本节不涉及上述内容 |
| 34Dxx Stability theory for ordinary differential equations [See also 37C75, 93Dxx] 34D05 Asymptotic properties of solutions to ordinary differential equations 34D06 Synchronization of solutions to ordinary differential equations 34D08 Characteristic and Lyapunov exponents of ordinary differential equations 34D09 Dichotomy, trichotomy of solutions to ordinary differential equations 34D10 Perturbations of ordinary differential equations 34D15 Singular perturbations of ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34D23 Global stability of solutions to ordinary differential equations 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations [See also 37C20] 34D35 Stability of manifolds of solutions to ordinary differential equations 34D45 Attractors of solutions to ordinary differential equations [See also 37C70, 37D45] 34D99 None of the above, but in this section |
34Dxx 常微分方程稳定性理论 [另见 37C75,93Dxx] 34D05 常微分方程解的渐近性质 34D06 常微分方程解的同步性 34D08 常微分方程特征值与李雅普诺夫指数 34D09 常微分方程解的二分法与三分法 34D10 常微分方程的摄动 34D15 常微分方程的奇异摄动 34D20 常微分方程解的稳定性 34D23 常微分方程解的全局稳定性 34D30 常微分方程解的结构稳定性与类似概念 [另见 37C20] 34D35 常微分方程解流形的稳定性 34D45 常微分方程解的吸引子 [另见 37C70,37D45] 34D99 本节不涉及上述内容 |
| 34Exx Asymptotic theory for ordinary differential equations 34E05 Asymptotic expansions of solutions to ordinary differential equations 34E10 Perturbations, asymptotics of solutions to ordinary differential equations 34E13 Multiple scale methods for ordinary differential equations 34E15 Singular perturbations, general theory for ordinary differential equations 34E17 Canard solutions to ordinary differential equations 34E18 Methods of nonstandard analysis for ordinary differential equations 34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations 34E99 None of the above, but in this section |
34Exx 常微分方程渐近理论 34E05 常微分方程解的渐近展开 34E10 常微分方程解的摄动与渐近性 34E13 常微分方程多尺度方法 34E15 奇异性摄动与常微分方程一般理论 34E17 常微分方程的卡纳德解 34E18 常微分方程非标准分析方法 34E20 奇异性摄动、拐点理论与常微分方程 WKB 方法 34E99 本节不涉及上述内容 |
| 34Fxx Ordinary differential equations and systems with randomness [See also 34K50, 60H10, 93E03] 34F05 Ordinary differential equations and systems with randomness [See also 34K50, 60H10, 93E03] 34F10 Bifurcation of solutions to ordinary differential equations involving randomness 34F15 Resonance phenomena for ordinary differential equations involving randomness 34F99 None of the above, but in this section |
34Fxx 常微分方程与随机系统 [另见 34K50、60H10、93E03] 34F05 常微分方程与随机系统 [另见 34K50、60H10、93E03] 34F10 随机常微分方程解的分岔现象 34F15 随机常微分方程的共振现象 34F99 本节不涉及上述内容 |
| 34Gxx Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25] 34G10 Linear differential equations in abstract spaces [See also 47D06, 47D09] 34G20 Nonlinear differential equations in abstract spaces [See also 47Hxx, 47Jxx] 34G25 Evolution inclusions 34G99 None of the above, but in this section |
34Gxx 抽象空间中的微分方程 [另见 34Lxx、37Kxx、47Dxx、47Hxx、47Jxx、58D25] 34G10 抽象空间中的线性微分方程 [另见 47D06、47D09] 34G20 抽象空间中的非线性微分方程 [另见 47Hxx、47Jxx] 34G25 演化包含 34G99 本节不涉及上述内容 |
| 34Hxx Control problems including ordinary differential equations [See also 49J15, 49K15, 93C15] 34H05 Control problems involving ordinary differential equations [See also 49J15, 49K15, 93C15] 34H10 Chaos control for problems involving ordinary differential equations 34H15 Stabilization of solutions to ordinary differential equations 34H20 Bifurcation control of ordinary differential equations 34H99 None of the above, but in this section |
34Hxx 包含常微分方程的控制问题 [另见 49J15、49K15、93C15] 34H05 涉及常微分方程的控制问题 [另见 49J15、49K15、93C15] 34H10 涉及常微分方程的混沌控制 34H15 常微分方程解的稳定化 34H20 常微分方程的分岔控制 34H99 本节不涉及上述内容 |
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34Kxx Functional-differential equations (including equations with delayed, ad-vanced or state-dependent argument)
34K04 Symmetries, invariants of functional-differentialequations [See also 37C79] 34K05 General theory of functional-differential equa-tions
34K06 Linear functional-differential equations
34K07 Theoretical approximation of solutions tofunctional-differential equations
34K08 Spectral theory of functional-differential opera-tors
34K09 Functional-differential inclusions
34K10 Boundary value problems for functional-differential equations
34K11 Oscillation theory of functional-differential equa-tions
34K12 Growth, boundedness, comparison of solutions tofunctional-differential equations [See also 37C35]
34K13 Periodic solutions to functional-differential equa-tions
[See also 37C27]
34K14 Almost and pseudo-almost periodic solutions tofunctional-differential equations
34K16 Heteroclinic and homoclinic orbits of functional-differential
equations [See also 37C29]
34K17 Transformation and reduction of functional-differential
equations and systems, normal forms
34K18 Bifurcation theory of functional-differentialequations [See also 37Gxx]
34K19 Invariant manifolds of functional-differentialequations
34K20 Stability theory of functional-differential equa-tions[See also 37C75]
34K21 Stationary solutions of functional-differentialequations
34K23 Complex (chaotic) behavior of solutions tofunctional-differential equations [See also 37D45]
34K24 Synchronization of functional-differential equa-tions
34K25 Asymptotic theory of functional-differentialequations
34K26 Singular perturbations of functional-differentialequations
34K27 Perturbations of functional-differential equations34K29 Inverse problems for functional-differential equa-tions
34K30 Functional-differential equations in abstractspaces [See also 34Gxx, 35R09, 35R10, 47Jxx]
34K31 Lattice functional-differential equations
34K32 Implicit functional-differential equations
34K33 Averaging for functional-differential equations
34K34 Hybrid systems of functional-differential equa-tions
34K35 Control problems for functional-differential equations [See also 49J21, 49K21, 93C23]
34K36 Fuzzy functional-differential equations
34K37 Functional-differential equations with fractionalderivatives
34K38 Functional-differential inequalities
34K39 Discontinuous functional-differential equations
34K40 Neutral functional-differential equations
34K41 Functional-differential equations in the complexdomain
34K42 Functional-differential equations on time scalesor measure chains
34K43 Functional-differential equations with state-dependent arguments
34K45 Functional-differential equations with impulses
34K50 Stochastic functional-differential equations [Seealso 34Fxx, 60Hxx]
34K60 Qualitative investigation and simulation of mod-els involving functional-differential equations
34K99 None of the above, but in this section
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34Kxx 功能微分方程（包括延迟型、超前型方程）或状态相关参数 34K04 对称性，泛函微分方程的不变量 [另见 37C79]
34K05 功能微分方程的一般理论
34K06 线性泛函微分方程
34K07 一阶泛函微分方程解的理论近似
34K08 有理函数微分算子的谱理论
34K09 功能性差异性包涵体
34K10 功能微分方程的边界值问题方程式
34K11 功能微分方程的振荡理论
34K12 增长、有界性、泛函微分方程解的比较[另见37C35]
34K13 功能微分方程的周期解[另见37C27]
34K14 几乎和伪几乎周期解在泛函微分方程中的应用
34K16 功能性微分的异斜与同斜轨道方程[另见37C29]
34K17 功能差异的转化与降低方程和系统，范式
34K18 功能微分方程的分岔理论 [另见 37Gxx]
34K19 功能微分方程不变流形
34K20 功能微分方程的稳定性理论[另见37C75]
34K21 功能微分方程的定常解
34K23 功能微分方程解的复杂（混沌）行为[另见37D45]
34K24 功能微分方程的同步化
34K25 泛函微分方程的渐近理论
34K26 功能微分方程的奇异摄动 34K27 功能微分方程的扰动34K29 功能微分方程的逆问题
34K30 抽象空间中的泛函微分方程[另见34Gxx、35R09、35R10、47Jxx]
34K31格点泛函微分方程
34K32 隐函数微分方程
34K34 功能微分方程的平均化
34K34 功能微分方程混合系统
34K35 泛函微分方程的控制问题[另见49J21、49K21、93C23]
34K36 模糊泛函微分方程
34K37 分式导数的函数微分方程
34K38 功能性差异不等式
34K39 不连续函数微分方程
34K40 中性功能微分方程
34K41 复变域中的泛函微分方程
34K42 时间尺度或测度链上的函数微分方程
34K43 带状态依赖项的函数微分方程争论
34K45 带冲激项的函数微分方程
34K50 随机泛函微分方程 [另见 34Fxx，60Hxx]
34K60模型的定性研究与仿真涉及函数微分方程
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34Lxx Ordinary differential operators [See also 47E05]
34L05 General spectral theory of ordinary differentialoperators
34L10 Eigenfunctions, eigenfunction expansions, com-pleteness
of eigenfunctions of ordinary differentialoperators
34L15 Eigenvalues, estimation of eigenvalues, upper andlower bounds of ordinary differential operators
34L16 Numerical approximation of eigenvalues and ofother parts of the spectrum of ordinary differentialoperators
34L20 Asymptotic distribution of eigenvalues, asymp-totic
theory of eigenfunctions for ordinary differen-tial
operators
34L25 Scattering theory, inverse scattering involving or-dinary
differential operators
34L30 Nonlinear ordinary differential operators
34L40 Particular ordinary differential operators (Dirac,one-dimensional Schr¨odinger, etc.)
34L99 None of the above, but in this section
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34Lxx 常微分算子 [参见也见于47E05] 34L05 常微分算子的一般谱论
34L10 本征函数，本征函数展开，完备性常微分算子的本征函数
34L15 特征值、特征值估计、常微分算子的上下界
34L16 一般微分算子特征值及谱的其他部分的数值逼近
34L20 本征值的渐近分布常微分方程本征函数理论经营者
34L25 散射理论，涉及普通逆散射微分算子
34L30 非线性常微分算子
34L40 特定常微分算子（狄拉克算子、一维薛定谔算子等）
34L99 本节不涉及上述内容
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34Mxx Ordinary differential equations in the complex domain [See also 30Dxx]32G34]
34M03 Linear ordinary differential equations and sys-tems in the complex domain
34M04 Nonlinear ordinary differential equations and systems in the complex domain
34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
34M10 Oscillation, growth of solutions to ordinary dif-ferential equations in the complex domain
34M15 Algebraic aspects (differential-algebraic, hyper-transcendence, group-theoretical) of ordinary differential equations in the complex domain
34M25 Formal solutions and transform techniques for ordinary differential equations in the complex do-main
34M30 Asymptotics and summation methods for ordinary differential equations in the complex domain
34M35 Singularities, monodromy and local behavior ofsolutions to ordinary differential equations in thecomplex domain, normal forms
34M40 Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equa-tions in the complex domain
34M45 Ordinary differential equations on complex manifolds34M46 Spectral theory for ordinary differential opera-tors in the complex domain
34M50 Inverse problems (Riemann-Hilbert, inverse dif-ferential Galois, etc.) for ordinary differential equations in the complex domain
34M55 Painlev´e and other special ordinary differentialequations in the complex domain; classification, hi-erarchies
34M56 Isomonodromic deformations for ordinary differential equations in the complex domain
34M60 Singular perturbation problems for ordinary dif-ferential equations in the complex domain (complexWKB, turning points, steepest descent) [See also34E20]
34M65 Topological structure of trajectories of ordinarydifferential equations in the complex domain
34M99 None of the above, but in this section
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34Mxx 常微分方程复合结构域[另见30Dxx]32G34] 34M03 线性常微分方程与系统复数域
34M04 非线性常微分方程与复数域系统
34M05 通解与亚纯解复变域微分方程
34M10 振荡，常微分方程的解的增长复数域方程
34M15 代数方面（微分代数、超超越性）常微分群论方程式复数域
34M25 正式解决方案与转换技术复数域上的常微分方程
34M30 常微分方程的渐近法与求和法复变域微分方程
34M35 复变域中常微分方程解的奇点、单值性与局部行为及标准型
34M40 复域常微分方程的斯托克斯现象与联络问题（线性和非线性）
34M45常微分方程 34M46 常微分算子的谱理论复数域
34M50 逆问题（黎曼-希尔伯特，逆微分伽罗瓦等) 普通微分方程复数域
34M55 Painlev方程及其他复变域特殊常微分方程的分类与层次结构
34M56 常微分方程的等单值变形复数域方程
34M60 常微分方程的奇异摄动问题复数域中的方程（复数WKB法、拐点法、最陡下降法）[另见34E20]
34M65 复域中常微分方程轨迹的拓扑结构
34M99 本节不涉及上述内容
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34Nxx Dynamic equations on time scales or measure chains {For real analysis on time scales, see 26E70}
34N05 Dynamic equations on time scales or measurechains {For real analysis on time scales or measurechains, see 26E70} 34N99 None of the above, but in this section
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34Nxx 时间尺度上的动力学方程或测度链{关于实分析时间尺度，见26E70} 34N05 时间尺度或测度链上的动力学方程 {关于时间尺度或测度链上的实分析，参见26E70}
34N99 本节不涉及上述内容
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35-XX Partial differential equations
35-00 General reference works (handbooks, dictionaries,bibliographies, etc.) pertaining to partial differential equations
35-01 Introductory exposition (textbooks, tutorial pa-pers, etc.) pertaining to partial differential equations
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35-03 History of partial differential equations [Consideralso classification numbers pertaining to Section 01]35-04 Software, source code, etc. for problems pertain-ing
to partial differential equations
35-06 Proceedings, conferences, collections, etc. per-taining
to partial differential equations
35-11 Research data for problems pertaining to partialdifferential equations
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35-XX 偏微分方程 35-00 与偏微分相关的通用参考文献（手册、词典、参考书目等）方程式
35-01 引言性阐述（教材、教程论文，等)偏微分方程
35-02 关于偏微分方程的论述（专著、综述）
35-03 偏微分方程的历史 [另请参阅第01节的分类编号] |
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35Axx General topics in partial differential equations
35A01 Existence problems for PDEs: global existence,local existence, non-existence
35A02 Uniqueness problems for PDEs: global unique-ness, local uniqueness, non-uniqueness
35A08 Fundamental solutions to PDEs
35A09 Classical solutions to PDEs
35A10 Cauchy-Kovalevskaya theorems
35A15 Variational methods applied to PDEs
35A16 Topological and monotonicity methods appliedto PDEs
35A17 Parametrices in context of PDEs
35A18 Wave front sets in context of PDEs
35A20 Analyticity in context of PDEs
35A21 Singularity in context of PDEs
35A22 Transform methods (e.g., integral transforms)applied to PDEs
35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals35A24 Methods of ordinary differential equations applied to PDEs
35A25 Other special methods applied to PDEs
35A27 Microlocal methods and methods of sheaf theoryand homological algebra applied to PDEs [See also32C38, 58J15]
35A30 Geometric theory, characteristics, transformations in context of PDEs [See also 58J70, 58J72]
35A35 Theoretical approximation in context of PDEs{For numerical analysis, see 65Mxx, 65Nxx}
35A99 None of the above, but in this section
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35Axx 偏微分方程中的一般性问题方程式 35A01 假设PDE存在性问题：全局存在性、局部存在性、不存在性
35A02 偏微分方程的唯一性问题：全局唯一性局部唯一性
35A08 基本解
35A09 常微分方程的古典解柯西-科瓦列夫斯卡娅定理
35A15 变分方法在偏微分方程中的应用
35A16 拓扑方法与单调性方法在偏微分方程中的应用
35A17 偏微分方程中的参数化
35A18 波前在偏微分方程中的背景设定
35A20 偏微分方程中的解析性
35A21 偏微分方程中的奇点
35A22 应用于偏微分方程的变换方法（如积分变换）
35A23 不等式在涉及导数的偏微分方程中的应用微分与积分算子，或积分35A24 常微分方程的求解方法到偏微分方程
35A25 应用于偏微分方程的其他特殊方法
35A27 微局部方法与束理论及同调代数在偏微分方程中的应用[另见32C38,58J15]
35A30 几何理论、特性、变换在PDEs的背景下[另见58J70、58J72]
35A35 偏微分方程背景下的理论近似{数值分析参见65Mxx、65Nxx}
35A99 本节不涉及上述内容
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35Bxx Qualitative properties of solutions to partial differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35B06 Symmetries, invariants, etc. in context of PDEs35B07 Axially symmetric solutions to PDEs
35B08 Entire solutions to PDEs
35B09 Positive solutions to PDEs
35B10 Periodic solutions to PDEs
35B15 Almost and pseudo-almost periodic solutions toPDEs
35B20 Perturbations in context of PDEs
35B25 Singular perturbations in context of PDEs
35B27 Homogenization in context of PDEs; PDEs inmedia with periodic structure [See also 74Q05,74Q10, 76M50, 78M40, 80M40]
35B30 Dependence of solutions to PDEs on initialand/or boundary data and/or on parameters ofPDEs [See also 37Cxx]
35B32 Bifurcations in context of PDEs [See also 34C23,34F10, 34H20, 37F46, 37Gxx, 37H20, 35J20, 37L10,37M20, 47J15, 58E05, 58E07, 58J55, 74G60, 74H60]35B33 Critical exponents in context of PDEs
35B32 Bifurcations in context of PDEs [See also 34C23,34F10, 34H20, 37F46, 37Gxx, 37H20, 35J20, 37L10,37M20, 47J15, 58E05, 58E07, 58J55, 74G60, 74H60]35B33 Critical exponents in context of PDEs35B34 Resonance in context of PDEs [See also 34F15,70J40, 70K28, 70K30, 81U24]
35B35 Stability in context of PDEs [See also 34Dxx,37B25, 37C20, 37C75, 37F15, 37J25, 37K45, 37L15,49K40, 58K25, 93Dxx]
35B36 Pattern formations in context of PDEs [See also92C15]
35B38 Critical points of functionals in context of PDEs(e.g., energy functionals) [See also 57R70, 58K05,58E05]
35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors [See also 34D45, 37B35, 37C70,37D45, 37G35, 37L30, 37M22]
35B42 Inertial manifolds [See also 37L25]
35B44 Blow-up in context of PDEs
35B45 A priori estimates in context of PDEs
35B50 Maximum principles in context of PDEs
35B51 Comparison principles in context of PDEs
35B53 Liouville theorems and Phragm´en-Lindel¨of theorems in context of PDEs
35B60 Continuation and prolongation of solutions toPDEs [See also 58A15, 58A17, 58Hxx]
35B65 Smoothness and regularity of solutions to PDEs35B99 None of the above, but in this section
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35Bxx 溶液的定性性质关于偏微分方程 35B05 振荡、解的零点、平均值定理等在偏微分方程（PDEs）的语境中
35B06 偏微分方程中的对称性、不变量等概念35B07 偏微分方程的轴对称解
35B08 偏微分方程的完整解决方案
35B09 偏微分方程的正解
35B10 偏微分方程的周期解
35B15 基于PDEs的几乎和伪几乎周期解
35B20 常微分方程背景下的扰动
35B25 偏微分方程中的奇异摄动
35B27 周期结构中的PDEs均质化；具有周期结构的PDEs [另见74Q05、74Q10、76M50、78M40、80M40]
35B30 偏微分方程（PDE）解对初始数据、边界数据及方程参数的依赖性[另见37Cxx]
35B32 偏微分方程（PDE）背景下的分岔现象[另见34C23、34F10、34H20、37F46、37Gxx、37H20、35J20、37L10、37M20、47J15、58E05、58E07、58J55、74G60、74H60]35B33 偏微分方程背景下的临界指数
35B34 常微分方程背景下的共振现象 [另见 34F15,70J40,70K28,70K30,81U24]
35B35 偶发性癫痫（PDEs）背景下的稳定性[另见 34Dxx、37B25、37C20、37C75、37F15、37J25、37K45、37L15、49K40、58K25、93Dxx]
35B36 常微分方程背景下的模式形成[另见92C15]
35B38 偏微分方程（PDEs）背景下泛函的关键点（如能量泛函）[另见57R70、58K05、58E05]
35B40 偏微分方程解的渐近行为
35B41 吸引子 [另见 34D45、37B35、37C70、37D45、37G35、37L30、37M22]
35B42 惯性流形 [另见 37L25]
35B44 偏微分方程背景下的爆破
35B45 偏微分方程背景下的先验估计
35B50 偏微分方程背景下的最大值原理
35B51 偏微分方程背景下的比较原则 35B53 刘维尔定理与弗拉格门-林德勒夫定理在PDEs的背景下
35B60 偏微分方程解的延拓与推广 [另见 58A15、58A17、58Hxx] 35B65 偏微分方程解的光滑性与正则性
35B99 本节不涉及上述内容 |
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35Cxx Representations of solutions to partial differential equations
35C05 Solutions to PDEs in closed form
35C06 Self-similar solutions to PDEs
35C07 Traveling wave solutions
35C08 Soliton solutions [See also 37K40]
35C09 Trigonometric solutions to PDEs
35C10 Series solutions to PDEs
35C11 Polynomial solutions to PDEs
35C15 Integral representations of solutions to PDEs
35C20 Asymptotic expansions of solutions to PDEs
35C99 None of the above, but in this section
|
35Cxx 部分解的表示微分方程 35C05 闭式解的偏微分方程
35C06 偶次方程的自相似解
35C07 旅行波解
35C08 孤子解 [另见 37K40]
35C09 偏微分方程的三角函数解
35C10 系列偏微分方程求解器
35C11 偏微分方程的多项式解
35C15 偏微分方程解的积分表示
35C20 偏微分方程解的渐近展开
35C99 本节不涉及上述内容
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35Dxx Generalized solutions to partial differential equations
35D30 Weak solutions to PDEs
35D35 Strong solutions to PDEs
35D40 Viscosity solutions to PDEs
35D99 None of the above, but in this section
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35Dxx 偏微分方程的通解方程式 35D30 偏微分方程的弱解
35D35 偏微分方程的强解
35D40 用于偏微分方程的粘性解
35D99 本节不涉及上述内容
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35Exx Partial differential equations and systems of partial differential equations with constant coefficients [See also 35N05]
35E05 Fundamental solutions to PDEs and systems ofPDEs with constant coefficients 35E10 Convexity properties of solutions to PDEs andsystems of PDEs with constant coefficients
35E15 Initial value problems for PDEs and systems ofPDEs with constant coefficients
35E20 General theory of PDEs and systems of PDEswith constant coefficients
35E99 None of the above, but in this section
|
35Exx偏微分方程和偏微分方程组恒定系数[另见35N05] 35E05 常系数偏微分方程及系统的基本解
35E10 常系数偏微分方程及其系统解的凸性性质
35E15 常系数偏微分方程及系统初值问题
35E20 常系数偏微分方程及系统的一般理论
35E99 本节不涉及上述内容
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35Fxx General first-order partial differential equations and systems of first-order partial differential equations
35F05 Linear first-order PDEs
35F10 Initial value problems for linear first-order PDEs35F15 Boundary value problems for linear first-orderPDEs
35F16 Initial-boundary value problems for linear first-order PDEs
35F20 Nonlinear first-order PDEs
35F21 Hamilton-Jacobi equations {For calculus of varia-tions and optimal control, see 49Lxx; for mechanicsof particles and systems, see 70H20}
35F25 Initial value problems for nonlinear first-orderPDEs
35F30 Boundary value problems for nonlinear first-orderPDEs
35F31 Initial-boundary value problems for nonlinearfirst-order PDEs
35F35 Systems of linear first-order PDEs
35F40 Initial value problems for systems of linear first-order PDEs
35F45 Boundary value problems for systems of linearfirst-order PDEs
35F46 Initial-boundary value problems for systems oflinear first-order PDEs
35F50 Systems of nonlinear first-order PDEs
35F55 Initial value problems for systems of nonlinearfirst-order PDEs
35F60 Boundary value problems for systems of nonlinear first-order PDEs
35F61 Initial-boundary value problems for systems ofnonlinear first-order PDEs
35F99 None of the above, but in this section
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35Fxx 一阶偏微分方程一阶方程和方程组偏微分方程 35F05 线性一阶偏微分方程
35F10 线性一阶偏微分方程的初值问题35F15 线性一阶偏微分方程的边值问题
35F16 线性一阶初边值问题PDE
35F20 非线性一阶偏微分方程
35F21 Hamilton-Jacobi方程{变分法关于最优控制，参见49Lxx；关于粒子与系统的力学，参见70H20}
35F25 非线性一阶偏微分方程的初值问题
35F30 非线性一阶偏微分方程的边界值问题
35F31 非线性一阶偏微分方程的初边值问题
35F35 线性一阶偏微分方程组
35F40 线性一阶系统初值问题PDE
35F45 线性一阶偏微分方程组的边界值问题
35F46 线性一阶偏微分方程组的初边值问题
35F50 非线性一阶偏微分方程组
35F55 非线性一阶偏微分方程组的初值问题
35F60 非线性系统边值问题一阶偏微分方程
35F61 非线性一阶偏微分方程组的初边值问题
35F99 本节不涉及上述内容
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35Gxx General higher-order partial differential equations and systems of higher-order partial differential equations
35G05 Linear higher-order PDEs
35G10 Initial value problems for linear higher-orderPDEs
35G15 Boundary value problems for linear higher-orderPDEs
35G16 Initial-boundary value problems for linearhigher-order PDEs
35G20 Nonlinear higher-order PDEs
35G25 Initial value problems for nonlinear higher-orderPDEs35G30 Boundary value problems for nonlinear higher-order PDEs
35G31 Initial-boundary value problems for nonlinearhigher-order PDEs
35G35 Systems of linear higher-order PDEs
35G40 Initial value problems for systems of linearhigher-order PDEs
35G45 Boundary value problems for systems of linearhigher-order PDEs
35G46 Initial-boundary value problems for systems oflinear higher-order PDEs
35G50 Systems of nonlinear higher-order PDEs
35G55 Initial value problems for systems of nonlinearhigher-order PDEs
35G60 Boundary value problems for systems of nonlin-ear higher-order PDEs
35G61 Initial-boundary value problems for systems ofnonlinear higher-order PDEs
35G99 None of the above, but in this section
|
35Gxx 通用高阶偏微分高阶方程和方程组偏微分方程 35G05 线性高阶偏微分方程
35G10 线性高阶偏微分方程的初值问题
35G15 线性高阶偏微分方程的边界值问题
35G16 线性高阶偏微分方程的初边值问题
35G20 非线性高阶偏微分方程
35G25 非线性高阶偏微分方程的初值问题
35G30 非线性高阶边值问题PDE
35G31 非线性高阶偏微分方程的初边值问题
35G35线性高阶偏微分方程组
35G40 线性高阶偏微分方程组的初值问题
35G45 线性高阶偏微分方程组的边界值问题
35G46 线性高阶偏微分方程组的初边值问题
35G50 高阶非线性偏微分方程组
35G55 非线性高阶偏微分方程组的初值问题
35G60 非线性系统边值问题高阶偏微分方程
35G61 非线性高阶偏微分方程组的初边值问题
35G99 本节不涉及上述内容
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35Hxx Close-to-elliptic equations
35H10 Hypoelliptic equations 35H20 Subelliptic equations
35H30 Quasielliptic equations
35H99 None of the above, but in this section
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35Hxx 近椭圆方程 35H10 低椭圆方程
35H20 亚椭圆方程
35H30 准椭圆方程
35H99 本节不涉及上述内容
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35Jxx Elliptic equations and elliptic systems {For global analysis, analysis on man-ifolds,
see 58J10, 58J20}
35J05 Laplace operator, Helmholtz equation (reducedwave equation), Poisson equation [See also 31Axx,31Bxx]
35J08 Green’s functions for elliptic equations
35J10 Schr¨odinger operator, Schr¨odinger equation {Forordinary differential equations, see 34L40; for op-erator
theory, see 47D08; for quantum theory, see81Q05; for statistical mechanics, see 82B44}
35J15 Second-order elliptic equations
35J20 Variational methods for second-order ellipticequations
35J25 Boundary value problems for second-order ellipticequations
35J30 Higher-order elliptic equations [See also 31A30,31B30]
35J35 Variational methods for higher-order ellipticequations
35J40 Boundary value problems for higher-order ellipticequations
35J46 First-order elliptic systems
35J47 Second-order elliptic systems
35J48 Higher-order elliptic systems
35J50 Variational methods for elliptic systems
35J56 Boundary value problems for first-order ellipticsystems
35J57 Boundary value problems for second-order ellipticsystems
35J58 Boundary value problems for higher-order ellipticsystems
35J60 Nonlinear elliptic equations
35J61 Semilinear elliptic equations
35J62 Quasilinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35J66 Nonlinear boundary value problems for nonlinearelliptic equations
35J67 Boundary values of solutions to elliptic equationsand elliptic systems
35J70 Degenerate elliptic equations
35J75 Singular elliptic equations
35J86 Unilateral problems for linear elliptic equationsand variational inequalities with linear elliptic operators [See also 35R35, 49J40]
35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators [See also 35R35, 49J40]
35J88 Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators [See also 35R35, 49J40]
35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35J92 Quasilinear elliptic equations with p-Laplacian
35J93 Quasilinear elliptic equations with mean curva-ture operator
35J94 Elliptic equations with infinity-Laplacian
35J96 Monge-Amp`ere equations {For complex Monge-Amp`ere operators, see 32W20; for parabolic Monge-Amp`ere equations, see 35K96}
35J99 None of the above, but in this section
|
35Jxx 椭圆方程与椭圆系统{针对全局分析，对流形的分析，见58J10、58J20 35J05 拉普拉斯算子、亥姆霍兹方程（约化波动方程）、泊松方程[另见31Axx、31Bxx]
35J08 椭圆型方程的格林函数
35J10 舍罗丁算子，舍罗丁方程{关于常微分方程，参见34L40；关于算子理论部分参见47D08；量子理论部分参见81Q05；统计力学部分参见82B44
35J15 二阶椭圆方程
35J20 二阶椭圆型方程的变分方法
35J25 二阶椭圆型方程的边界值问题
35J30 高阶椭圆方程 [另见 31A30,31B30]
35J35 高阶椭圆方程的变分方法
35J40 高阶椭圆型方程的边界值问题
35J46 一阶椭圆系统
35J47 二阶椭圆系统
35J48 高阶椭圆系统
35J50 椭圆型系统的变分方法
35J56 一阶椭圆型系统的边界值问题
35J57 二阶椭圆型系统的边界值问题
35J58 高阶椭圆型系统的边界值问题
35J60 非线性椭圆方程
35J61 半线性椭圆方程
35J62 拟线性椭圆方程
35J65 线性椭圆型非线性边值问题方程式
35J66 非线性椭圆型方程的非线性边值问题
35J67 椭圆方程和椭圆方程组的解的边界值
35J70 退化椭圆方程
35J75奇异椭圆方程 35J86 线性椭圆方程和变分不等式的一边问题[另见35R35、49J40]
35J87 非线性椭圆方程的单边问题以及含非线性椭圆项的变分不等式操作员[另见35R35、49J40]
35J88 椭圆系和系统的单边问题含椭圆算子的变分不等式[另见35R35、49J40]
35J91 含Laplacian、bi-Laplacian的半线性椭圆方程或多拉普拉斯
35J92 p-Laplacian拟线性椭圆方程
35J93 带平均曲率的拟线性椭圆方程经营者
35J94 无穷拉普拉斯椭圆方程
35J96 蒙日-安培方程{复变蒙日-安培方程算子，参见32W20；关于抛物型蒙日-安培方程，见35K96}
35J99 本节不涉及上述内容
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35Kxx Parabolic equations and parabolic systems {For global analysis, analysis on manifolds, see 58J35}
35K05 Heat equation
35K08 Heat kernel
35K10 Second-order parabolic equations
35K15 Initial value problems for second-order parabolicequations
35K20 Initial-boundary value problems for second-orderparabolic equations
35K25 Higher-order parabolic equations
35K30 Initial value problems for higher-order parabolicequations
35K35 Initial-boundary value problems for higher-orderparabolic equations
35K40 Second-order parabolic systems
35K41 Higher-order parabolic systems
35K45 Initial value problems for second-order parabolicsystems
35K46 Initial value problems for higher-order parabolicsystems
35K51 Initial-boundary value problems for second-orderparabolic systems
35K52 Initial-boundary value problems for higher-orderparabolic systems
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations {For diffusion pro-cesses and reaction effects, see 47D07, 58J65,60J60, 60J70, 74N25, 76R50, 76V05, 80A23, 82B24,82C24, 92E20}
35K58 Semilinear parabolic equations
35K59 Quasilinear parabolic equations
35K60 Nonlinear initial, boundary and initial-boundaryvalue problems for linear parabolic equations
35K61 Nonlinear initial, boundary and initial-boundaryvalue problems for nonlinear parabolic equations
35K65 Degenerate parabolic equations
35K67 Singular parabolic equations
35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
35K85 Unilateral problems for linear parabolic equations
and variational inequalities with linearparabolic operators [See also 35R35, 49J40]
35K86 Unilateral problems for nonlinear parabolic equations
and variational inequalities with nonlinearparabolic operators [See also 35R35, 49J40]
35K87 Unilateral problems for parabolic systems and systems of variational inequalities with parabolicoperators [See also 35R35, 49J40]
35K90 Abstract parabolic equations
35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
35K92 Quasilinear parabolic equations with p-Laplacian35K93 Quasilinear parabolic equations with mean cur-vature operator
35K96 Parabolic Monge-Amp`ere equations
35K99 None of the above, but in this section
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35 Kxx抛物方程与抛物线系统{针对全局分析，对流形，参见58J35} 35K05 热方程
35K08 热核
35K10 二阶抛物型方程
35K15 二阶抛物型方程的初值问题二阶抛物型方程的35K20 初边值问题
35K25 高阶抛物方程
35K30 高阶抛物型方程的初值问题
35K35 高阶抛物型方程的初边值问题
35K40 二阶抛物型系统
35K41 高阶抛物线系统
35K45 二阶抛物型系统的初值问题
35K46 高阶抛物型方程组的初值问题 35K51 二阶抛物型系统的初边值问题
35K52 高阶抛物型方程组的初边值问题
35K55 非线性抛物方程
35K57 反应扩散方程{扩散过程及反应效应，参见47D07、58J65、60J60、60J70、74N25、76R50、76V05、80A23、82B24、82C24、92E20
35K58 半线性抛物方程
35K59 准线性抛物方程
35K60 线性抛物型方程的非线性初边值和初边值问题
35K61 非线性抛物型方程的非线性初边值问题
35K65 简并抛物方程
35K67 奇异抛物方程
35K70 超抛物线方程、拟抛物线方程等
35K85 线性抛物方程的单边问题以及含线性抛物型算子的变分不等式[另见35R35、49J40]
35K86 非线性抛物型方程的单边问题以及含非线性抛物型算子的变分不等式[另见35R35、49J40]
35K87 双曲型系统及含双曲算子变分不等式系统的单边问题[另见35R35、49J40]
35K90 抽象抛物方程
35K91 拉普拉斯、双拉普拉斯或多拉普拉斯的半线性抛物方程
35K92 具有p-Laplacian算子的拟线性抛物方程35K93具有平均曲率的拟线性抛物方程经营者
35K96 抛物型蒙格-安培方程
35K99 本节不涉及上述内容
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35Lxx Hyperbolic equations and hyper-bolic systems {For global analysis, see 58J45}
35L02 First-order hyperbolic equations 35L03 Initial value problems for first-order hyperbolic equations
35L04 Initial-boundary value problems for first-order hyperbolic equations
35L05 Wave equation
35L10 Second-order hyperbolic equations
35L15 Initial value problems for second-order hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L25 Higher-order hyperbolic equations
35L30 Initial value problems for higher-order hyperbolic equations
35L35 Initial-boundary value problems for higher-order hyperbolic equations
35L40 First-order hyperbolic systems
35L45 Initial value problems for first-order hyperbolic systems
35L50 Initial-boundary value problems for first-order hyperbolic systems
35L51 Second-order hyperbolic systems
35L52 Initial value problems for second-order hyperbolic systems
35L53 Initial-boundary value problems for second-order hyperbolic systems
35L55 Higher-order hyperbolic systems
35L56 Initial value problems for higher-order hyperbolic systems
35L57 Initial-boundary value problems for higher-order hyperbolic systems
35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations [See also 58Kxx, 74J40, 76L05]
35L70 Second-order nonlinear hyperbolic equations
35L71 Second-order semilinear hyperbolic equations
35L72 Second-order quasilinear hyperbolic equations
35L75 Higher-order nonlinear hyperbolic equations
35L76 Higher-order semilinear hyperbolic equations
35L77 Higher-order quasilinear hyperbolic equations
35L80 Degenerate hyperbolic equations
35L81 Singular hyperbolic equations
35L82 Pseudohyperbolic equations
35L85 Unilateral problems for linear hyperbolic equa-tions and variational inequalities with linear hyper-bolic operators [See also 35R35, 49J40]
35L86 Unilateral problems for nonlinear hyperbolicequations and variational inequalities with nonlin-ear hyperbolic operators [See also 35R35, 49J40]
35L87 Unilateral problems for hyperbolic systems andsystems of variational inequalities with hyperbolicoperators [See also 35R35, 49J40]
35L90 Abstract hyperbolic equations
35L99 None of the above, but in this section
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35Lxx 双曲线方程与双曲系统{关于全球分析，请参见58J45} 35L02 一阶双曲方程
35L03 一阶双曲型初值问题方程式
35L04 一阶初边值问题双曲方程
35L05 波方程
35L10 二阶双曲方程
35L15 二阶双曲型初值问题方程式二阶35L20初边值问题双曲方程
35L25 高阶双曲方程
35L30 高阶双曲型初值问题方程式
35L35 高阶初边值问题双曲方程
35L40 一阶双曲型系统
35L45 一阶双曲型初值问题系统
35L50 一阶初边值问题双曲系统
35L51 二阶双曲型系统
35L52 二阶双曲型初值问题系统
35L53 二阶初边值问题双曲系统
35L55 高阶双曲系统
35L56 高阶双曲型初值问题系统
35L57 高阶初边值问题双曲系统
35L60 一阶非线性双曲方程
35L65 双曲守恒定律
35L67 双曲方程的激波与奇点[另见58Kxx、74J40、76L05]
35L70 二阶非线性双曲方程
35L71 二阶半线性双曲方程
35L72 二阶拟线性双曲方程
35L75 高阶非线性双曲方程
35L76 高阶半线性双曲方程
35L77 高阶拟线性双曲方程
35L80 退化双曲方程
35L81奇异双曲方程
35L82 伪双曲方程
35L85 线性双曲方程的单边问题以及线性双曲型变分不等式操作[另见35R35、49J40]
35L86 非线性双曲方程和变分不等式的一边问题双曲算子
35L87 双曲型系统及含双曲算子变分不等式系统的单边问题[另见35R35、49J40]
35L90 摘要双曲方程
35L99 本节不涉及上述内容
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35Mxx Partial differential equations of mixed type and mixed-type systems of partial differential equations
35M10 PDEs of mixed type 35M11 Initial value problems for PDEs of mixed type
35M12 Boundary value problems for PDEs of mixedtype
35M13 Initial-boundary value problems for PDEs ofmixed type
35M30 Mixed-type systems of PDEs
35M31 Initial value problems for mixed-type systems ofPDEs
35M32 Boundary value problems for mixed-type sys-tems of PDEs
35M33 Initial-boundary value problems for mixed-typesystems of PDEs
35M85 Unilateral problems for linear PDEs of mixedtype and variational inequalities with partial dif-ferential operators of mixed type [See also 35R35,49J40]
35M86 Unilateral problems for nonlinear PDEs of mixedtype and variational inequalities with nonlinear partial differential operators of mixed type [See also35R35, 49J40]
35M87 Unilateral problems for mixed-type systems ofPDEs and systems of variational inequalities with partial differential operators of mixed type [See also35R35, 49J40]
35M99 None of the above, but in this section
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35Mxx 偏微分方程混合型和混合型系统偏微分方程
35M10混合型PDE
35M11 混合型偏微分方程初值问题
35M12 混合型偏微分方程的边界值问题
35M13 混合型偏微分方程初边值问题
35M30 混合型偏微分方程系统
35M31 混合型偏微分方程组的初值问题
35M32 混合型系统的边界值问题关于偏微分方程
35M33 混合型偏微分方程组的初边值问题
35M85 混合型线性偏微分方程和变分不等式的一边问题混合型操作者[另见35R35,49J40]
35M86 混合型非线性偏微分方程和变分不等式的一边问题混合型微分算子[另见35R35,49J40]
35M87 混合型偏微分方程系统及混合型偏微分算子变分不等式系统的单边问题[另见35R35,49J40]
35M99 本节不涉及上述内容
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35Nxx Overdetermined problems for partial differential equations and systems of partial differential equations {For global analysis, see 58Hxx, 58J10, 58J15}
35N05 Overdetermined systems of PDEs with constantcoefficients
35N10 Overdetermined systems of PDEs with variablecoefficients
35N15 ∂-Neumann problems and formal complexes incontext of PDEs [See also 32W05, 32W10, 58J10]
35N20 Overdetermined initial value problems for PDEsand systems of PDEs
35N25 Overdetermined boundary value problems forPDEs and systems of PDEs
35N30 Overdetermined initial-boundary value problemsfor PDEs and systems of PDEs
35N99 None of the above, but in this section
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35Nxx 部分过定问题微分方程和系统偏微分方程{针对全局分析，参见58Hxx、58J10、58J15} 35N05 常系数偏微分方程组的超定系统
35N10 变系数偏微分方程的超定系统
35N15 ∂-Neumann问题与偏微分方程中的形式复形[另见32W05、32W10、58J10]
35N20 偏微分方程和偏微分方程组的超定初值问题
35N25 偏微分方程及偏微分方程组的超定边值问题
35N30 偏微分方程及偏微分方程组的超定初边值问题
35N99 本节不涉及上述内容
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35Pxx Spectral theory and eigenvalue problems for partial differential equations {For operator theory, see 47Axx, 47Bxx, 47F05}
35P05 General topics in linear spectral theory for PDEs35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35P15 Estimates of eigenvalues in context of PDEs
35P20 Asymptotic distributions of eigenvalues in con-text of PDEs
35P25 Scattering theory for PDEs [See also 47A40]
35P30 Nonlinear eigenvalue problems and nonlinearspectral theory for PDEs
35P99 None of the above, but in this section
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35Pxx 光谱理论与本征值偏微分方程问题关于算子理论，可参阅47Axx、47Bxx章节。47F05} 35P05 常微分方程线性谱理论中的一般性问题35P10 本征函数的完备性与本征函数偏微分方程的展开
35P15 偏微分方程中特征值的估计
35P20 矩阵特征值的上下文渐近分布关于偏微分方程
35P25 偏微分方程的散射理论 [另见 47A40]
35P30 非线性特征值问题与偏微分方程的非线性谱理论
35P99 本节不涉及上述内容
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35Qxx Partial differential equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]
35Q05 Euler-Poisson-Darboux equations
35Q07 Fuchsian PDEs
35Q15 Riemann-Hilbert problems in context of PDEs[See also 30E25, 31A25, 31B20]
35Q20 Boltzmann equations {For fluid mechanics, see76P05; for statistical mechanics, see 82B40, 82C40,82D05}
35Q30 Navier-Stokes equations {For fluid mechanics,see 76D05, 76D07, 76N10}
35Q31 Euler equations {For fluid mechanics, see 76D05,76D07, 76N10}
35Q35 PDEs in connection with fluid mechanics
35Q40 PDEs in connection with quantum mechanics
35Q41 Time-dependent Schr¨odinger equations andDirac equations {For quantum theory, see 81Q05;for relativity and gravitational theory, see 83A05,83C10}
35Q49 Transport equations {For calculus of variationsand optimal control, see 49Q22; for fluid mechan-ics, see 76F25; for statistical mechanics, see 82C70,82D75; for operations research, see 90B06; formathematical programming, see 90C08}
35Q51 Soliton equations {For dynamical systems and ergodic theory, see 37K40}
35Q53 KdV equations (Korteweg-de Vries equations){For dynamical systems and ergodic theory, see37K10}
35Q55 NLS equations (nonlinear Schr¨odinger equations){For dynamical systems and ergodic theory, see37K10}
35Q56 Ginzburg-Landau equations {For optics and electromagnetic theory, see 78A25}
35Q60 PDEs in connection with optics and electromagnetic theory
35Q61 Maxwell equations {For optics and electromag-netic theory, see 78A25; for relativity and gravita-tional theory, see 83C22}
35Q62 PDEs in connection with statistics
35Q68 PDEs in connection with computer science
35Q70 PDEs in connection with mechanics of particlesand systems of particles
35Q74 PDEs in connection with mechanics of deformable solids
35Q75 PDEs in connection with relativity and gravitational theory
35Q76 Einstein equations {For several complex vari-ables and analytic spaces, see 32Q40; for differentialgeometry, see 53C07; for relativity and gravitationaltheory, see 83C05, 83C25, 83D05}
35Q79 PDEs in connection with classical thermodynamics and heat transfer
35Q81 PDEs in connection with semiconductor devices{For statistical mechanics, see 82D37}
35Q82 PDEs in connection with statistical mechanics
35Q83 Vlasov equations {For statistical mechanics, see82C70, 82D75}
35Q84 Fokker-Planck equations {For fluid mechanics,see 76X05, 76W05; for statistical mechanics, see82C31}
35Q85 PDEs in connection with astronomy and astro-physics
35Q86 PDEs in connection with geophysics
35Q89 PDEs in connection with mean field game theory{For calculus of variations and optimal control, see49N80; for game theory, see 91A16}
35Q90 PDEs in connection with mathematical program-ming
35Q91 PDEs in connection with game theory, eco-nomics, social and behavioral sciences
35Q92 PDEs in connection with biology, chemistry andother natural sciences
35Q93 PDEs in connection with control and optimization
35Q94 PDEs in connection with information and communication
35Q99 None of the above, but in this section
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35Qxx 偏微分方程数学物理及其他领域应用程序[另见35J05、35J10、35K05、35L05] 35Q05 欧拉-泊松-达布方程 35Q07 福克斯偏微分方程 35Q15 常微分方程背景下的黎曼-希尔伯特问题[另见30E25、31A25、31B20] 35Q20 玻尔兹曼方程 {流体力学参见76P05；统计力学参见82B40、82C40、82D05} 35Q30 纳维-斯托克斯方程 {流体力学相关参见76D05、76D07、76N10} 35Q31 欧拉方程组 {流体力学相关参见76D05、76D07、76N10} 35Q35流体力学中的PDE 35Q40 与量子力学相关的偏微分方程 35Q41 时间依赖的薛定谔方程与狄拉克方程 {量子理论参见81Q05；相对论与引力理论参见83A05、83C10} 35Q49 运输方程 {变分法与最优控制参见49Q22；流体力学参见 参见76F25；统计力学参见82C70、82D75；运筹学参见90B06；数学规划参见90C08 35Q51孤子方程{关于动力系统和遍历性 理论，见37K40} 35Q53 KdV方程（Korteweg-de Vries方程）{关于动力系统与遍历理论，参见37K10} 35Q55 NLS方程（非线性薛定谔方程）{关于动力系统与遍历理论，参见37K10} 35Q56金兹堡-朗道方程{光学和电磁学理论，见78A25} 35Q60 光学与电磁学中的偏微分方程理论 35Q61麦克斯韦方程组{光学与电磁学理论，参见78A25；关于相对论与引力理论，参见83C22} 35Q62 与统计学相关的偏微分方程 35Q68与计算机科学相关的偏微分方程 35Q70 与粒子及粒子系统力学相关的偏微分方程 35Q74 与可变形力学相关的偏微分方程固体 35Q75 PDEs与相对论和引力理论 35Q76爱因斯坦方程{关于若干复变量分析空间参见32Q40；微分几何参见53C07；相对论与引力理论参见83C05、83C25、83D05。 35Q79 PDEs与经典热力学以及传热 35Q81 与半导体器件相关的偏微分方程{统计力学相关内容参见82D37} 35Q82 与统计力学相关的偏微分方程 35Q83 弗拉索夫方程 {关于统计力学，参见82C70、82D75} 35Q84 福克-普朗克方程 {流体力学相关参见76X05、76W05；统计力学相关参见82C31} 35Q85 与天文学和天体物理学有关的PDE 35Q86 与地球物理学有关的偏微分方程 35Q89 与平均场博弈论相关的偏微分方程{关于变分法与最优控制，参见49N80；关于博弈论，参见91A16} 35Q89 与平均场博弈论相关的偏微分方程{关于变分法与最优控制，参见49N80；关于博弈论，参见91A16} 35Q90 PDEs与数学规划 35Q91 与博弈论、生态经济学相关的偏微分方程社会行为科学 35Q92 与生物学、化学及其他自然科学相关的偏微分方程 35Q93 与控制和优化相关的PDEs 35Q94 信息与通信中的偏微分方程 35Q99 本节不涉及上述内容 |
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35Rxx Miscellaneous topics in partial differential equations {For equations on man-ifolds, see 32Wxx, 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDEs, see 60H15}
35R01 PDEs on manifolds [See also 32Wxx, 53Cxx,58Jxx] 35R02 PDEs on graphs and networks (ramified or polygonal spaces)
35R03 PDEs on Heisenberg groups, Lie groups, Carnotgroups, etc.
35R05 PDEs with low regular coefficients and/or lowregular data
35R06 PDEs with measure
35R07 PDEs on time scales
35R09 Integral partial differential equations [See also45Kxx]
35R10 Functional partial differential equations
35R11 Fractional partial differential equations
35R12 Impulsive partial differential equations
35R13 Fuzzy partial differential equations
35R15 PDEs on infinite-dimensional (e.g., function)spaces (= PDEs in infinitely many variables) [Seealso 46Gxx, 58D25]
35R20 Operator partial differential equations (= PDEson finite-dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03,47D06, 47D09, 47H20, 47Jxx]
35R25 Ill-posed problems for PDEs
35R30 Inverse problems for PDEs
35R35 Free boundary problems for PDEs
35R37 Moving boundary problems for PDEs
35R45 Partial differential inequalities and systems ofpartial differential inequalities
35R50 PDEs of infinite order
35R60 PDEs with randomness, stochastic partial differential equations [See also 60H15]
35R70 PDEs with multivalued right-hand sides
35R99 None of the above, but in this section
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35Rxx 部分微分中的杂项问题关于流形方程组参见32Wxx、58Jxx；关于流形的解参见58Bxx；对于随机偏微分方程（PDEs），见60H15} 35R01 流形上的PDEs [另见32Wxx、53Cxx、58Jxx] 35R02 图论与网络上的偏微分方程（分支型或多边形型）空间 35R03 海森堡群、李群、卡诺群等上的PDEs 35R05 常规系数低和/或低常规数据的PDEs 35R06 带测度的偏微分方程 35R07 PDEs在时间尺度上的表现 35R09 全积分偏微分方程 [另见45Kxx] 35R10 功能性偏微分方程 35R11 分式偏微分方程 35R12 脉冲型偏微分方程 35R13 模糊偏微分方程 35R15 无限维空间（如函数空间）上的偏微分方程（即无限多个变量的偏微分方程）[另见46Gxx、58D25] 35R20 算子偏微分方程（=抽象空间值有限维空间上的偏微分方程）功能）[另见34Gxx、47A50、47D03、47D06、47D09、47H20、47Jxx] 35R25 偏微分方程的不适定问题 35R30 偏微分方程的逆问题 35R35 偏微分方程的自由边界问题 35R37 偏微分方程的移动边界问题 35R45 偏微分不等式与偏微分不等式系统 35R50 无限阶PDE 35R60 带随机性的偏微分方程方程式[另见60H15] 35R70 多值右侧的偏微分方程 35R99 本节不涉及上述内容 |
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35Sxx Pseudodifferential operators and other generalizations of partial differential
operators {For operator theory, see 47G30, 58J40} 35S05 Pseudodifferential operators as generalizationsof partial differential operators [See also 32W25,47G30, 47L80, 58J40] 35S10 Initial value problems for PDEs with pseudodifferential operators 35S15 Boundary value problems for PDEs with pseudodifferential operators 35S16 Initial-boundary value problems for PDEs with pseudodifferential operators 35S30 Fourier integral operators applied to PDEs [Seealso 43A32, 58J40] 35S35 Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology,stratified sets, etc. [See also 32C38, 32S40, 32S60,58J15] 35S50 Paradifferential operators as generalizations ofpartial differential operators in context of PDEs 35S99 None of the above, but in this section |
35S05 假微分算子作为偏微分算子的推广[另见32W25、47G30、47L80、58J40] 35S10 带伪微分的偏微分方程初值问题操作 35S15 带伪微分的偏微分方程的边界值问题操作 含伪微分算子的偏微分方程的35S16初边值问题 35S30 傅里叶积分算子在偏微分方程中的应用[另见43A32、58J40] 35S35 伪微分算子的拓扑性质 在偏微分方程（PDEs）的语境下：交上同调、分层集等[另见32C38、32S40、32S60、58J15] 35S50 作为偏微分算子推广的Paradifferential算子在偏微分方程中的应用 35S99 本节不涉及上述内容 |
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37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XX]
37-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to dynamical systems and ergodic theory
37-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37-03 History of dynamical systems and ergodic theory [Consider also classification numbers pertaining to Section 01]
37-04 Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory
37-06 Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory
37-11 Research data for problems pertaining to dynamical systems and ergodic theory
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37-XX 动力学系统与遍历理论 [另见 26A18，28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] 37-00 通用参考文献（手册、词典、参考文献等) 动力学系统遍历理论 37-01 引言性阐述（教材、教程论文，等) 与动力系统相关遍历理论 37-02 研究性论文（专著、综述）动力系统与遍历理论 37-03 动力学系统与遍历理论史[另需考虑与分类编号相关的第01节] 37-04 针对相关问题的软件、源代码等动力系统与遍历理论 37-06 会议记录、会议资料、文集等动力系统与遍历理论 37-11 动力学相关问题的研究数据系统与遍历理论 |
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37Axx Ergodic theory [See also 28Dxx]
37A05 Dynamical aspects of measure-preserving transformations
37A10 Dynamical systems involving one-parameter continuous families of measure-preserving transforma-tions
37A15 General groups of measure-preserving transformations and dynamical systems [See mainly 22Fxx]37A17 Homogeneous flows [See also 22Fxx]
37A20 Algebraic ergodic theory, cocycles, orbit equiva-lence, ergodic equivalence relations
37A25 Ergodicity, mixing, rates of mixing
37A30 Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly47A35}
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37A40 Nonsingular (and infinite-measure preserving)transformations
37A44 Relations between ergodic theory and numbertheory [See also 11Kxx]
37A46 Relations between ergodic theory and harmonicanalysis
37A50 Dynamical systems and their relations with probability theory and stochastic processes [See also60Fxx, 60G10]
37A55 Dynamical systems and the theory of C∗-algebras [See mainly 46L55]
37A60 Dynamical aspects of statistical mechanics [Seealso 82Cxx]
37A99 None of the above, but in this section
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37Axx 埃尔戈迪理论 [另见 28Dxx] 37A05 保测度变换的动力学性质 37A10 含单参数连续函数的动力系统保测变换族 37A15 测度保持变换的广义群以及动力系统[参见22Fxx]37A17齐次流[另见22Fxx] 37A20 代数遍历理论、上同调、轨道等价性遍历等价关系 37A25 呈遍性、混合、混合速率 37A30 呈遍性定理、谱论、马尔可夫算子 {关于算子遍历理论，参见主要47A35} 37A35 熵及其他不变量、同构、分类遍历理论 37A40 非奇异（保测度）变换 37A44 遍历理论与数论的关系[另见11Kxx] 37A46 遍历理论与调和分析的关系 37A50 动力学系统及其与概率的关系理论和随机过程[另见60Fxx，60G10] 37A55 动力学系统与C理论∗-代数[主要参见46L55] 37A60 统计力学的动态特性 [另见 82Cxx] 37A99 本节不涉及上述内容 |
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37Bxx Topological dynamics
37B02 Dynamics in general topological spaces 37B05 Dynamical systems involving transformationsand group actions with special properties (minimal-ity, distality, proximality, expansivity, etc.) 37B10 Symbolic dynamics 37B15 Dynamical aspects of cellular automata {Forcomputational aspects, see 68Q80} 37B20 Notions of recurrence and recurrent behavior indynamical systems 37B25 Stability of topological dynamical systems 37B30 Index theory for dynamical systems, Morse-Conley indices 37B35 Gradient-like and recurrent behavior; isolated(locally maximal) invariant sets; attractors, repellers for topological dynamical systems 37B40 Topological entropy 37B45 Continua theory in dynamics 37B51 Multidimensional shifts of finite type 37B52 Tiling dynamics 37B55 Topological dynamics of nonautonomous systems37B65 Approximate trajectories, pseudotrajectories,shadowing and related notions for topological dynamical systems 37B99 None of the above, but in this section |
37Bxx 拓扑动力学 37B02 一般拓扑空间中的动力学 37B05 涉及变换与群作用的特殊性质（最小性）的动力系统远端性、近端性、扩张性等) 37B10 符号动力学 37B15 细胞自动机的动力学特性 {计算方面参见68Q80} 37B20 动态系统中的复发与复发行为概念 37B25 拓扑动力系统的稳定性 37B30 动力学系统指数理论，莫尔斯-康利索引 37B35 梯度样与复发行为；孤立（局部最大）不变集；吸引子、排斥子拓扑动力系统 37B40 拓扑熵 37B45 动力学中的连续理论 37B51 有限型多维移位 37B52 瓦片动力学 37B55 非自治系统的拓扑动力学37B65 拓扑动力学中的近似轨迹、伪轨迹、影射及相关概念系统 37B99 本节不涉及上述内容 |
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37Cxx Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
37C10 Dynamics induced by flows and semiflows
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
37C20 Generic properties, structural stability of dynamical systems
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics
37C27 Periodic orbits of vector fields and flows
37C29 Homoclinic and heteroclinic orbits for dynamical systems
37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transferoperators, etc.
37C35 Orbit growth in dynamical systems
37C40 Smooth ergodic theory, invariant measures forsmooth dynamical systems [See also 37Dxx]
37C45 Dimension theory of smooth dynamical systems37C50 Approximate trajectories (pseudotrajectories,shadowing, etc.) in smooth dynamics
37C55 Periodic and quasi-periodic flows and diffeomorphisms
37C60 Nonautonomous smooth dynamical systems [Seealso 37B55]
37C65 Monotone flows as dynamical systems
37C70 Attractors and repellers of smooth dynamicalsystems and their topological structure
37C75 Stability theory for smooth dynamical systems
37C79 Symmetries and invariants of dynamical systems[See also 34C14, 34K04]
37C81 Equivariant dynamical systems
37C83 Dynamical systems with singularities (billiards,etc.)
37C85 Dynamics induced by group actions other than Z and R, and C [See mainly 22Fxx, and also 32M25,57R30, 57Sxx]
37C86 Foliations generated by dynamical systems
37C99 None of the above, but in this section
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37Cxx光滑动力系统：一般理论[另见34Cxx、34Dxx] 37C05 涉及光滑映射的动力系统微分同胚 37C10 流与半流引起的动力学 37C15 拓扑与可微等价性、共轭性模 37C20 通用特性，动力学结构稳定性系统 37C25 动力学的不动点与周期点系统； 定点指数理论，局部动力学 37C27 向量场与流的周期轨道 37C29 动力学中的同宿轨道与异宿轨道系统 37C30 动态系统中的功能分析技术；ζ函数、(Ruelle-Frobenius)转移算子等。 37C35 动力学系统中的轨道增长 37C40 平滑遍历理论，光滑动力系统的不变测度[另见37Dxx] 37C45 光滑动力系统的尺寸理论37C50光滑动力学中的近似轨迹（伪轨迹、影迹等） 37C55 周期和准周期流与微分同胚 37C60 非自治光滑动力系统[另见37B55] 37C65 单调流作为动力系统 37C70 光滑动力系统的吸引子与排斥子及其拓扑结构 37C75光滑动力系统的稳定性理论 37C79 动力学系统的对称性与不变量[另见34C14、34K04] 37C81 等变动力系统 37C83 带有奇点的动力系统（如台球系统等） 37C85 由Z以外的群作用诱导的动力学 以及R和C[主要参见22Fxx，另见32M25,57R30、57Sxx] 37C86 动力学系统生成的叶状结构 37C99 本节不涉及上述内容 |
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37Dxx Dynamical systems with hyperbolic behavior
37D05 Dynamical systems with hyperbolic orbits andsets 37D10 Invariant manifold theory for dynamical systems37D15 Morse-Smale systems 37D20 Uniformly hyperbolic systems (expanding,Anosov, Axiom A, etc.) 37D25 Nonuniformly hyperbolic systems (Lyapunov ex-ponents, Pesin theory, etc.) 37D30 Partially hyperbolic systems and dominatedsplittings 37D35 Thermodynamic formalism, variational princi-ples,
equilibrium states for dynamical systems
37D40 Dynamical systems of geometric origin and hy-perbolicity
(geodesic and horocycle flows, etc.)
37D45 Strange attractors, chaotic dynamics of systemswith hyperbolic behavior
37D99 None of the above, but in this section
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37Dxx 双曲型动力系统行为 37D05具有双曲轨道和集合的动力系统动力系统不变流形理论37D10 莫尔斯-斯梅尔系统 37D20 均匀双曲系统（扩张型、Anosov型、公理A型等） 37D25 不均匀双曲系统（Lyapunov指数，佩辛理论等。) 37D30 部分双曲系统与支配分裂 37D35 热力学形式体系、变分原理动力系统平衡态 37D40 几何起源和双曲性的动力系统（测地流与轨道流等） 37D45 异常吸引子，具有双曲行为的系统的混沌动力学 37D99 本节不涉及上述内容 |
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37Exx Low-dimensional dynamical systems
37E05 Dynamical systems involving maps of the interval(piecewise continuous, continuous, smooth) 37E10 Dynamical systems involving maps of the circle37E15 Combinatorial dynamics (types of periodic or-bits) 37E20 Universality and renormalization of dynamicalsystems [See also 37F25] 37E25 Dynamical systems involving maps of trees andgraphs 37E30 Dynamical systems involving homeomorphismsand diffeomorphisms of planes and surfaces 37E35 Flows on surfaces 37E40 Dynamical aspects of twist maps 37E45 Rotation numbers and vectors 37E99 None of the above, but in this section |
37Exx低维动力系统 37E05 涉及区间映射的动力系统（分段连续、连续、光滑） 37E10 涉及圆周映射的动力系统37E15 组合动力学（周期或比特的类型） 37E20 动力系统的普适性与重整化[另见37F25] 37E25 涉及树和图映射的动力系统 37E30 平面和曲面的同胚与微分同胚的动态系统 37E35 表面流动 37E40 扭转图的动态特性 37E45 旋转数与向量 37E99 本节不涉及上述内容 |
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37Fxx Dynamical systems over complex numbers [See also 30D05, 32H50]
37F05 Dynamical systems involving relations and correspondences in one complex variable 37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets [See also 32A10, 32A20, 32H02, 32H04] 37F12 Critical orbits for holomorphic dynamical systems 37F15 Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems 37F20 Combinatorics and topology in relation with holomorphic dynamical systems 37F25 Renormalization of holomorphic dynamical systems 37F31 Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics 37F32 Fuchsian and Kleinian groups as dynamical systems 37F34 Teichmu¨ller theory; moduli spaces of holomorphic dynamical systems 37F35 Conformal densities and Hausdorff dimension forholomorphic dynamical systems 37F40 Geometric limits in holomorphic dynamics 37F44 Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps37F46 Bifurcations; parameter spaces in holomorphicdynamics; the Mandelbrot and Multibrot sets 37F50 Small divisors, rotation domains and linearization in holomorphic dynamics 37F75 Dynamical aspects of holomorphic foliations andvector fields [See also 32M25, 32S65, 34Mxx] 37F80 Higher-dimensional holomorphic and meromorphic dynamics 37F99 None of the above, but in this section |
37Fxx 动力系统复数域上的数字[另见30D05、32H50] 37F05 关系和对应关系的动态系统一个复变数 37F10 复多项式与有理数的动力学映射、全函数与亚纯函数；法图与Julia组[另见32A10、32A20、32H02、32H04] 37F12全纯动力系统的临界轨道 37F15 扩张全纯映射； 双曲性；全纯动力系统的结构稳定性 37F20 组合学与拓扑学的关系全纯动力系统 37F25 全纯动力系统的重正规化 37F31 全纯动力学中的拟共形方法拟共形动力学 37F32 动力学系统中的Fuchsian群和Kleinian群 37F34 Teichmu¨ller理论；全纯模空间动力系统 37F35 全纯动力系统的共形密度与豪斯多夫维数 37F40 全纯动力学中的几何极限 37F44 动力学系统的全纯族；全纯运动；全纯映射半群37F46 分岔；全纯动力学中的参数空间；曼德勃罗集与多重曼德勃罗集 37F50 小的除数、旋转域与线性化全纯动力学 37F75 全纯叶状结构与向量场的动力学特性 [另见 32M25、32S65、34Mxx] 37F80 高维全纯与亚纯动力学 37F99 本节不涉及上述内容 |
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37Gxx Local and nonlocal bifurcation theory for dynamical systems [See also 34C23, 34K18]
37G05 Normal forms for dynamical systems 37G10 Bifurcations of singular points in dynamical systems 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems 37G20 Hyperbolic singular points with homoclinic trajectories in dynamical systems 37G25 Bifurcations connected with nontransversal intersection in dynamical systems 37G30 Infinite nonwandering sets arising in bifurcations of dynamical systems 37G35 Dynamical aspects of attractors and their bifurcations 37G40 Dynamical aspects of symmetries, equivariant bifurcation theory 37G99 None of the above, but in this section |
37Gxx 动力学系统局部与非局部分岔理论[另见34C23、34K18] 37G05 动力学系统的标准型 37G10 动力学系统奇点分岔 37G15 动力学系统极限环与周期轨道分岔 37G20 动力学系统具有同宿轨迹的双曲奇点 37G25 动力学系统非横截相交相关分岔 37G30 动力学系统分岔产生的无限非游荡集 37G35 吸引子及其分岔的动力学特性 37G40 对称性动力学特性与等变分岔理论 37G99 本节不涉及上述内容 |
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37Hxx Random dynamical systems [See also 15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx]
37H05 General theory of random and stochastic dynamical systems 37H10 Generation, random and stochastic differenceand differential equations [See also 34F05, 34K50,60H10, 60H15] 37H12 Random iteration 37H15 Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents [Seealso 34D08, 37Axx, 37Cxx, 37Dxx] 37H20 Bifurcation theory for random and stochastic dynamical systems [See also 37Gxx] 37H30 Stability theory for random and stochastic dynamical systems 37H99 None of the above, but in this section |
37Hxx 随机动力系统 [参见以及15B52、34D08、34F05、47B80、70L05, 82C05, 93Exx] 37H05 随机与随机动力学通论系统 37H10 代数、随机与随机微分方程及差分方程 [另见 34F05、34K50、60H10、60H15] 37H12 随机迭代 37H15 随机和随机动力学的多乘法随机动力系统研究遍历理论，李雅普诺夫指数[另见34D08、37Axx、37Cxx、37Dxx] 37H20 分岔理论系统[另见37Gxx] 37H30 稳定性理论系统 37H99 本节不涉及上述内容 |
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37Jxx Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems [See also 53Dxx, 70Fxx, 70Hxx]
37J06 General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants 37J11 Symplectic and canonical mappings 37J12 Fixed points and periodic points of finite-dimensional Hamiltonian and Lagrangian systems37J20 Bifurcation problems for finite-dimensionalHamiltonian and Lagrangian systems 37J25 Stability problems for finite-dimensional Hamil-tonian and Lagrangian systems 37J30 Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems(nonintegrability criteria) 37J35 Completely integrable finite-dimensional Hamil-tonian systems, integration methods, integrabilitytests 37J37 Relations of finite-dimensional Hamiltonian andLagrangian systems with Lie algebras and other al-gebraic structures 37J38 Relations of finite-dimensional Hamiltonian andLagrangian systems with algebraic geometry, com-plex analysis, special functions 37J39 Relations of finite-dimensional Hamiltonian andLagrangian systems with topology, geometry anddifferential geometry (symplectic geometry, Poissongeometry, etc.) [See also 53D20]
37J40 Perturbations of finite-dimensional Hamiltoniansystems, normal forms, small divisors, KAM the-ory, Arnol’d diffusion
37J46 Periodic, homoclinic and heteroclinic orbits offinite-dimensional Hamiltonian systems
37J51 Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems;variational principles; degree-theoretic methods
37J55 Contact systems [See also 53D10]
37J60 Nonholonomic dynamical systems [See also70F25]
37J65 Nonautonomous Hamiltonian dynamical systems(Painlev´e equations, etc.)
37J70 Completely integrable discrete dynamical systems
37J99 None of the above, but in this section |
37Jxx有限维空间中的动力学问题哈密顿和拉格朗日 系统[另见53Dxx、70Fxx、70Hxx] 37J06有限维哈密尔顿量的一般理论以及拉格朗日系统、哈密顿系统和拉格朗日系统结构、对称性、不变量 37J11辛映射与典范映射有限维空间的不动点与周期点 Hamiltonian和Lagrangian系统 37J20 有限维Hamiltonian和Lagrangian系统的分岔问题 37J25 有限维哈密顿量的稳定性问题以及拉格朗日系统有限维情形下37J30可积性障碍哈密顿和拉格朗日系统（不可积性判据） 37J35 完全可积的有限维哈密顿量系统，积分方法，可积性检验 37J37 有限维哈密顿和拉格朗日系统与李代数及其他代数的关系结构 37J38 有限维哈密顿和拉格朗日系统与代数几何、复 分析 37J39 有限维哈密顿系统与拉格朗日系统的拓扑、几何及微分几何（辛几何、泊松几何等）关系[另见53D20] 37J40 有限维哈密顿系统的扰动、正规形、小除子、Kam理论 Arnold弥散 37J46 有限维哈密顿周期、同宿和异宿轨道系统 37J51 有限维情形下的极小作用轨道与测度 哈密顿系统与拉格朗日系统；变分原理；度数理论方法 37J55 接触系统 [另见 53D10] 37J60 非完整动力系统 [另见70F25] 37J65 非自治哈密顿动力系统（Painlev‘e方程等） 37J70 完全可积离散动力系统 37J99 本节不涉及上述内容 |
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37Kxx Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian
systems [See also 35Axx, 35Qxx]
37K06 General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian
structures, symmetries, conservation laws37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integrationmethods, integrability tests, integrable hierarchies(KdV, KP, Toda, etc.)
37K15 Inverse spectral and scattering methods forinfinite-dimensional Hamiltonian and Lagrangiansystems
37K20 Relations of infinite-dimensional Hamiltonianand Lagrangian dynamical systems with algebraicgeometry, complex analysis, and special functions[See also 14H70]
37K25 Relations of infinite-dimensional Hamiltonianand Lagrangian dynamical systems with topology,geometry and differential geometry
37K30 Relations of infinite-dimensional Hamiltonianand Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
37K35 Lie-B¨acklund and other transformations forinfinite-dimensional Hamiltonian and Lagrangiansystems 37K40 Soliton theory, asymptotic behavior of solutionsof infinite-dimensional Hamiltonian systems 37K45 Stability problems for infinite-dimensionalHamiltonian and Lagrangian systems 37K50 Bifurcation problems for infinite-dimensionalHamiltonian and Lagrangian systems 37K55 Perturbations, KAM for infinite-dimensionalHamiltonian and Lagrangian systems 37K58 Variational principles and methods for infinite-dimensionalHamiltonian and Lagrangian systems 37K60 Lattice dynamics; integrable lattice equations[See also 37L60] 37K65 Hamiltonian systems on groups of diffeomor-phismsand on manifolds of mappings and metrics 37K99 None of the above, but in this section |
37Kxx 动力系统方面 无限维哈密顿量和拉格朗日量 系统[另见35Axx、35Qxx] 37K06 无限维哈密尔顿量的一般理论 以及拉格朗日系统、哈密顿系统和拉格朗日系统结构、对称性、守恒定律37K10 完全可积的无限维哈密顿系统与拉格朗日系统、积分方法、可积性判据、可积体系（KdV、KP、Toda等） 37K15 无限维哈密顿和拉格朗日系统的反谱与反散射方法 37K20 无限维哈密顿和拉格朗日动力系统与代数几何、复分析及特殊函数的关系[另见14H70] 37K25 无限维哈密顿和拉格朗日动力系统与拓扑、几何和微分几何的关系 37K30 无限维哈密顿和拉格朗日动力系统的无限维关系 Lie代数及其他代数结构 37K35 Lie-Bäcklund变换及其他无限维哈密顿与拉格朗日系统变换 37K40 孤子理论：无限维哈密顿系统解的渐近行为37K45 无限维哈密顿与拉格朗日系统的稳定性问题37K50 无限维哈密顿与拉格朗日系统的分岔问题37K55 无限维哈密顿与拉格朗日系统的摄动与Kam方法 37K58 无限维哈密顿与拉格朗日系统的变分原理与方法 37K60 晶格动力学：可积晶格方程[另见37L60] 37K65 微分同胚群及映射流形与度量流形上的哈密顿系统 37K99 本节不涉及上述内容 |
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37Lxx Infinite-dimensional dissipative dy-namical systems [See also 35Bxx, 35Qxx]
37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations 37L10 Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems
37L15 Stability problems for infinite-dimensional dissipative dynamical systems
37L20 Symmetries of infinite-dimensional dissipative dynamical systems
37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
37L30 Infinite-dimensional dissipative dynamical systems–attractors and their dimensions, Lyapunov exponents
37L40 Invariant measures for infinite-dimensional dissipative dynamical systems
37L45 Hyperbolicity; Lyapunov functions for infinite-dimensional dissipative dynamical systems
37L50 Noncompact semigroups; dispersive equations;perturbations of infinite-dimensional dissipative dynamical systems
37L55 Infinite-dimensional random dynamical systems;stochastic equations [See also 35R60, 60H10, 60H15]37L60 Lattice dynamics and infinite-dimensional dissipative
dynamical systems [See also 37K60]
37L65 Special approximation methods (nonlinearGalerkin, etc.) for infinite-dimensional dissipativedynamical systems
37L99 None of the above, but in this section
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37Lxx 无限维耗散动力学系统[另见35Bxx、35Qxx] 37L05 无限维耗散的一般理论动力系统，非线性半群，演化方程式 37L10 正则形、中心流形理论、分岔无限维耗散动力学理论系统 37L15 无限维耗散系统稳定性问题动力系统 37L20 无限维耗散对称性动力系统 37L25 惯性流形及其他不变吸引子无限维耗散动力学系统 37L30 无限维耗散动力学系统吸引子及其维数 倡导者 37L40 无限维耗散系统的不变量测度动力系统 37L45 双曲性； 无限维Lyapunov函数耗散动力系统 37L50 非紧致半群；色散方程；无限维耗散动力学的摄动系统 37L55 无限维随机动力系统；随机方程 [另见 35R60、60H10、60H15]37L60 晶格动力学与无限维耗散系统动力系统 37L65 无限维耗散动力系统特殊逼近方法(非线性Galerkin等) 37L99 本节不涉及上述内容 |
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37Mxx Approximation methods and numerical treatment of dynamical systems {For numerical analysis, see also 65Pxx; for software etc., see 37-04}
37M05 Simulation of dynamical systems 37M10 Time series analysis of dynamical systems 37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamicalsystems 37M20 Computational methods for bifurcation problems in dynamical systems 37M21 Computational methods for invariant manifoldsof dynamical systems 37M22 Computational methods for attractors of dynamical systems 37M25 Computational methods for ergodic theory (approximation of invariant measures, computation ofLyapunov exponents, entropy, etc.) 37M99 None of the above, but in this section |
37Mxx逼近方法与数值计算动力系统处理{关于数值分析，另见65Pxx；用于软件等。参见37-04} 37M05 动力学系统仿真 37M10 动力学系统的时间序列分析 37M15 离散化方法与积分器（辛方法，变分的、几何的等) 动力学系统 37M20 分岔问题的计算方法动力系统 37M21 动力学系统不变流形的计算方法 37M22 动力学吸引子的计算方法系统 37M25遍历理论的计算方法（近似）不变测度、Lyapunov指数、熵等的计算) 37M99 本节不涉及上述内容 |
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37Nxx Applications of dynamical systems
37N05 Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]
37N15 Dynamical systems in solid mechanics [Seemainly 74Hxx]
37N20 Dynamical systems in other branches of physics(quantum mechanics, general relativity, laserphysics)
37N25 Dynamical systems in biology [See also 92-XX]
37N30 Dynamical systems in numerical analysis [Seealso 65-XX]
37N35 Dynamical systems in control [See also 93-XX]
37N40 Dynamical systems in optimization and economics [See also 90-XX, 91-XX]
37N99 None of the above, but in this section
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37Nxx 动力学系统应用 37N05经典与天体力学中的动力系统[主要参见70Fxx、70Hxx、70Kxx] 37N10 流体力学中的动力系统，海洋学以及气象学[参见主要76-XX，特别是76D05, 76F20, 86A05, 86A10] 37N15 固体力学中的动力系统 [Seemainly 74Hxx] 37N20 物理学其他分支中的动力系统（量子力学、广义相对论、激光物理学） 37N25 生物学中的动力系统 [另见 92-XX] 37N30 数值分析中的动力系统 [另见 65-XX] 37N35 控制中的动力系统 [另见 93-XX] 37N40 动力学系统在优化和经济学中的应用[另见90-XX、91-XX] 37N99 本节不涉及上述内容 |
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37Pxx Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A44]
37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps 37P10 Arithmetic and non-Archimedean dynamical systems involving analytic and meromorphic maps
37P15 Dynamical systems over global ground fields
37P20 Dynamical systems over non-Archimedean localground fields
37P25 Dynamical systems over finite ground fields
37P30 Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems [See also 11G50, 14G40]
37P35 Arithmetic properties of periodic points
37P40 Non-Archimedean Fatou and Julia sets
37P45 Families and moduli spaces in arithmetic andnon-Archimedean dynamical systems
37P50 Dynamical systems on Berkovich spaces
37P55 Arithmetic dynamics on general algebraic vari-eties
37P99 None of the above, but in this section
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37Pxx 算术与非阿基米德数动力系统 37P05 算术与非阿基米德动力系统涉及多项式和有理映射 37P10 代数与非阿基米德动力系统解析与亚纯映射 37P15 全局地面场上的动力系统 37P20 非阿基米德局部基域上的动力系统 37P25 有限基域上的动力系统 37P30 高度函数；格林函数；不变测度算术和非阿基米德动力学系统[另见11G50、14G40] 37P35 周期点的算术性质 37P40 非阿基米德Fatou集与Julia集 37P45 算术与非阿基米德动力系统中的族与模空间 Berkovich空间上的37P50动力系统 37P55 一般代数簇上的算术动力学 37P99 本节不涉及上述内容 |
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39-XX Difference and functional equations
39-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to difference and functional equations 39-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations 39-02 Research exposition (monographs, survey articles) pertaining to difference and functional equations 39-03 History of difference and functional equations[Consider also classification numbers pertaining toSection 01] 39-04 Software, source code, etc. for problems pertaining to difference and functional equations 39-06 Proceedings, conferences, collections, etc. pertaining to difference and functional equations 39-08 Computational methods for problems pertainingto difference and functional equations 39-11 Research data for problems pertaining to difference and functional equations |
39-XX 差异与功能方程式 39-00 通用参考文献（手册、词典、参考文献等) 与差异相关泛函方程 39-01 引言性阐述（教材、教程论文，等)与差异及功能相关方程式 39-02 研究性论文（专著、综述）关于差分和泛函方程 39-03 差分与泛函方程的历史[另请参阅第01节中的分类编号] 39-04 针对相关问题的软件、源代码等差分方程和泛函方程 39-06 会议记录、会议资料、文集等差分方程和泛函方程 39-08 差分方程与泛函方程相关问题的计算方法 39-11 与差异相关问题的研究数据以及功能方程 |
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39Axx Difference equations {For dynamic equations on time scales, see 34N05; for dynamical systems, see 37-XX}
39A05 General theory of difference equations 39A06 Linear difference equations 39A10 Additive difference equations 39A12 Discrete version of topics in analysis 39A13 Difference equations, scaling (q-differences) [Seealso 33Dxx] 39A14 Partial difference equations 39A20 Multiplicative and other generalized differenceequations, e.g., of Lyness type 39A21 Oscillation theory for difference equations 39A22 Growth, boundedness, comparison of solutions todifference equations 39A23 Periodic solutions of difference equations 39A24 Almost periodic solutions of difference equations39A26 Fuzzy difference equations 39A27 Boundary value problems for difference equations39A28 Bifurcation theory for difference equations 39A30 Stability theory for difference equations 39A33 Chaotic behavior of solutions of difference equations 39A36 Integrable difference and lattice equations; interability tests 39A45 Difference equations in the complex domain 39A50 Stochastic difference equations 39A60 Applications of difference equations 39A70 Difference operators [See also 47B39] 39A99 None of the above, but in this section |
39Axx 差分方程 {用于动态时间尺度上的方程，参见34N05；动力系统，见37-XX} 39A05 差分方程通论 39A06 线性差分方程 39A10 附加差分方程 39A12 分析学专题的离散版本 39A13 差分方程，缩放（q-差分）[另见 33Dxx] 39A14 部分差分方程 39A20 乘法型及其他广义差分方程，例如g.林内斯型 39A21 一阶差分方程的振荡理论 39A22 有限增长、有界性、微分方程解的比较 39A23 差分方程的周期解 39A24 差分方程的几乎周期解39A26 模糊差分方程 39A27 差分方程的边界值问题39A28 差分方程的分岔理论 39A30 一阶差分方程的稳定性理论 39A33 一阶差分方程解的混沌行为 39A36 可积差分方程和格点方程； 可积性 试验 39A45 复变域中的差分方程 39A50 随机差分方程 39A60 差分方程的应用 39A70 差异运算符 [另见 47B39] 39A99 本节不涉及上述内容 |
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39Bxx Functional equations and inequalities [See also 30D05]
39B05 General theory of functional equations and inequalities
39B12 Iteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]
39B22 Functional equations for real functions [See also26A51, 26B25]
39B32 Functional equations for complex functions [Seealso 30D05]
39B42 Matrix and operator functional equations [Seealso 47Jxx]
39B52 Functional equations for functions with moregeneral domains and/or ranges
39B55 Orthogonal additivity and other conditionalfunctional equations
39B62 Functional inequalities, including subadditivity,convexity, etc. [See also 26A51, 26B25, 26Dxx]
39B72 Systems of functional equations and inequalities39B82 Stability, separation, extension, and related topics for functional equations [See also 46A22]
39B99 None of the above, but in this section
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39Bxx 功能方程与不等式[另见30D05] 39B05 功能方程与不等式的一般理论 39B12 迭代理论、迭代方程和复合方程 [另见26A18、30D05、37-XX] 39B22 实函数的函数方程 [另见26A51、26B25] 39B32 复变函数的函数方程 [另见 30D05] 39B42 矩阵与算子泛函方程 [另见 47Jxx] 39B52 适用于更广定义域和/或取值范围函数的函数方程 39B55 正交可加性及其他条件函数方程 39B62 功能不等式，包括次可加性、凸性等[另见26A51、26B25、26Dxx] 39B72 功能方程与不等式系统39B82 稳定性、分离、延拓及相关主题 用于功能方程[另见46A22] 39B99 本节不涉及上述内容 |
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40-XX Sequences, series, summability
40-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to sequences, series, summability
40-01 Introductory exposition (textbooks, tutorial pa-pers, etc.) pertaining to sequences, series, summa-bility
40-02 Research exposition (monographs, survey articles) pertaining to sequences, series, summability
40-03 History of sequences, series, summability [Con-sider also classification numbers pertaining to Section 01]
40-04 Software, source code, etc. for problems pertaining to sequences, series, summability
40-06 Proceedings, conferences, collections, etc. pertaining to sequences, series, summability
40-08 Computational methods for problems pertainingto sequences, series, summability
40-11 Research data for problems pertaining to se-quences, series, summability
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40-XX序列、系列、可加性 40-00 通用参考文献（手册、词典、参考文献等) 与序列、系列相关，可和性 40-01 引言性阐述（教材、教程论文，等) 与序列、级数、可加性有关 40-02 研究性文献（专著、综述文章）关于序列、级数、可和性的 40-03 序列、级数与可和性历史 [考虑以及与章节相关的分类编号01] 40-04 针对相关问题的软件、源代码等可和性 40-06 会议记录、会议资料、文集等可和性 40-08 序列、级数与可求和性问题的计算方法 40-11 关于序列相关问题的研究数据级数可和性 |
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40Bxx Multiple sequences and series
40B05 Multiple sequences and series (should also be as-signed
at least one other classification number inthis section)
40B99 None of the above, but in this sectio
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40Bxx 多个序列和系列 40B05 多个序列与系列（亦应进行分配）本节中至少一个其他分类编号） 40B99 本节不涉及上述内容 |
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40Cxx General summability methods
40C05 Matrix methods for summability 40C10 Integral methods for summability 40C15 Function-theoretic methods (including power series methods and semicontinuous methods) forsummability 40C99 None of the above, but in this section |
40Cxx 一般可积性方法 40C05 可加矩阵方法 40C10 可积的积分方法 40C15函数论方法（含幂级数）可加性方法和半连续方法 40C99 本节不涉及上述内容 |
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40Dxx Direct theorems on summability
40D05 General theorems on summability
40D09 Structure of summability fields
40D10 Tauberian constants and oscillation limits insummability theory
40D15 Convergence factors and summability factors
40D20 Summability and bounded fields of methods
40D25 Inclusion and equivalence theorems in summability
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40Dxx 可积性直接定理 40D05 可积性的一般定理 40D09 可加域的结构 可加性理论中的40D10陶伯常数和振荡极限 40D15 收敛因子与可加性因子 40D20 方法的可加性与有界域 40D25 可加性中的包含与等价定理 |
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40Exx Inversion theorems
40E05 Tauberian theorems, general
40E10 Growth estimates
40E15 Lacunary inversion theorems
40E20 Tauberian constants
40E99 None of the above, but in this section
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40Exx 反演定理 40E05 陶伯定理，一般 40E10 增长预测 40E15 缺陷反演定理 40E20 陶伯常数 40E99 本节不涉及上述内容 |
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40Fxx Absolute and strong summability (should also be assigned at least one other classification number in Section 40)
40F05 Absolute and strong summability (should also beassigned at least one other classification number inSection 40)
40F99 None of the above, but in this section
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40Fxx 绝对强可积性（还应至少分配另一个第40条分类编号 40F05 绝对且强可加性（还应在第40节中至少分配另一个分类编号） 40F99 本节不涉及上述内容 |
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40Gxx Special methods of summability
40G05 Ces`aro, Euler, N¨orlund and Hausdorff methods40G10 Abel, Borel and power series methods
40G15 Summability methods using statistical convergence [See also 40A35]
40G99 None of the above, but in this section
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40Gxx 可加性的特殊方法 40G05 Cesaro、Euler、Nörlund和Hausdorff方法40G10 Abel、Borel及幂级数方法 40G15统计收敛的可加性方法[另见40A35] 40G99 本节不涉及上述内容 |
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40Hxx Functional analytic methods in summability
40H05 Functional analytic methods in summability 40H99 None of the above, but in this section |
40Hxx 功能分析方法在可和性 40H05 可积性中的泛函分析方法 40H99 本节不涉及上述内容 |
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40Jxx Summability in abstract structures (should also be assigned at least one other
classification number from Section 40) [See also 43A55, 46A35, 46B15]
40J05 Summability in abstract structures (should alsobe assigned at least one other classification numberfrom Section 40) [See also 43A55, 46A35, 46B15]
40J99 None of the above, but in this section
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40Jxx抽象结构中的可加性（还应至少分配另一个 第40节分类编号）[参见以及43A55、46A35、46B15] 40J05 抽象结构中的可加性（应至少从第40部分分配另一个分类号）[另见43A55、46A35、46B15] 40J99 本节不涉及上述内容 |
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41-XX Approximations and expansions {For approximation theory in the complex domain, see 30E05, 30E10; for trigonometric approximation and interpolation, see 42A10, 42A15; for numerical approximation, see 65Dxx}
41-00 General reference works (handbooks, dictionaries,bibliographies, etc.) pertaining to approximationsand expansions
41-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to approximations and ex-pansions
41-02 Research exposition (monographs, survey articles)pertaining to approximations and expansions
41-03 History of approximations and expansions [Consider also classification numbers pertaining to Section 01]
41-04 Software, source code, etc. for problems pertaining to approximations and expansions
41-06 Proceedings, conferences, collections, etc. pertaining to approximations and expansions
41-11 Research data for problems pertaining to approximations and expansions
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41-XX 近似与展开{关于近似理论在复杂领域中，参见 30E05、30E10；用于三角函数近似和插值 参见42A10、42A15；关于数值近似，见65Dxx} 41-00 与近似和展开相关的通用参考文献（手册、词典、参考书目等） 41-01 引言性阐述（教材、教程论文，等) 与近似和展开有关 41-02 关于近似与展开的研究综述（专著、综述文章） 41-03 近似与展开的历史 [考虑以及与章节相关的分类编号 01] 41-04 针对相关问题的软件、源代码等至近似与展开 41-06 会议记录、会议资料、文集等至近似与展开 41-11 与近似相关问题的研究数据以及扩张 |
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41Axx Approximations and expansions {For approximation theory in the complex domain, see 30E05, 30E10; for trigonometric approximation and interpolation, see 42A10, 42A15; for numerical approxima-tion, see 65Dxx}
41A05 Interpolation in approximation theory [See also 42A15, 65D05]
41A10 Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10}
41A15 Spline approximation
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’ski˘ı-type inequalities)
41A20 Approximation by rational functions 41A21 Pad´e approximation
41A25 Rate of convergence, degree of approximation
41A27 Inverse theorems in approximation theory
41A28 Simultaneous approximation
41A29 Approximation with constraints
41A30 Approximation by other special function classes
41A35 Approximation by operators (in particular, by integral operators)
41A36 Approximation by positive operators
41A40 Saturation in approximation theory
41A44 Best constants in approximation theory
41A45 Approximation by arbitrary linear expressions
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
41A50 Best approximation, Chebyshev systems
41A52 Uniqueness of best approximation
41A55 Approximate quadratures
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41)
41A65 Abstract approximation theory (approximationin normed linear spaces and other abstract spaces)
41A80 Remainders in approximation formulas 41A81 Weighted approximation
41A99 None of the above, but in this section
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41Axx 近似与展开复变函数逼近理论域，参见30E05、30E10；关于三角函数近似和插值 42A10、42A15；用于数值近似，见65Dxx} 41A05 近似理论中的插值法 [另见42A15, 65D05] 41A10 多项式逼近 {关于逼近由三角多项式表示，参见42A10} 41A15 样条逼近 41A17 近似不等式（伯恩斯坦，杰克逊，Nikol斯基 ı 型不等式 41A20 有理函数逼近 41A21 帕德近似 41A25 收敛率，逼近度 41A27逼近理论中的反定理 41A28 同步逼近 41A29 约束条件下的近似 41A30 其他特殊函数类的逼近 41A35 算子逼近（特别是积分算子）经营者 41A36 正算子逼近 41A40 近似理论中的饱和问题 41A44逼近理论中的最佳常数 41A45 任意线性表达式的近似 41A46 任意非线性表达式逼近；宽度和熵 41A50 最佳逼近，切比雪夫系统 41A52 最佳逼近的唯一性 41A55 近似求积法 41A58系列扩展（例如Taylor系列、Lidstone系列） 但不是傅里叶级数 41A60 渐近近似，渐近展开（最陡下降法等）[另见30E15] 41A63 多维问题（亦应分配）至少一个其他分类编号来自第41条） 41A65抽象逼近理论（赋范线性空间及其他抽象空间中的逼近）41A80逼近公式中的余数 41A81 加权近似 41A99 本节不涉及上述内容 |
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42-XX Harmonic analysis on Euclidean spaces
42-00 General reference works (handbooks, dictionaries,bibliographies, etc.) pertaining to harmonic analysis on Euclidean spaces
42-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces
42-02 Research exposition (monographs, survey articles)pertaining to harmonic analysis on Euclidean spaces42-03 History of harmonic analysis on Euclidean spaces[Consider also classification numbers pertaining toSection 01]
42-04 Software, source code, etc. for problems pertaining to harmonic analysis on Euclidean spaces
42-06 Proceedings, conferences, collections, etc. pertaining to harmonic analysis on Euclidean spaces
42-08 Computational methods for problems pertainingto harmonic analysis on Euclidean spaces
42-11 Research data for problems pertaining to harmonic analysis on Euclidean spaces
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42-XX 欧氏空间的调和分析空间 42-00 关于谐波分析的通用参考文献（手册、词典、参考书目等）在欧几里得空间上的 42-01 引言性阐述（教材、教程论文，等)关于欧氏空间上的调和分析空间 42-02 欧几里得空间调和分析研究专著与综述论文 42-03 欧几里得空间调和分析发展史[另请参阅第01节相关分类号] 42-04 针对相关问题的软件、源代码等欧氏空间上的调和分析 42-06 会议记录、会议资料、文集等欧氏空间上的调和分析 42-08 欧几里得空间调和分析问题的计算方法 42-11 关于谐波问题的研究数据欧几里得空间分析 |
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42Axx Harmonic analysis in one variable
42A05 Trigonometric polynomials, inequalities, extremal problems
42A10 Trigonometric approximation
42A15 Trigonometric interpolation
42A16 Fourier coefficients, Fourier series of functionswith special properties, special Fourier series {Forautomorphic theory, see mainly 11F30}
42A20 Convergence and absolute convergence of Fourierand trigonometric series
42A24 Summability and absolute summability ofFourier and trigonometric series
42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
42A38 Fourier and Fourier-Stieltjes transforms andother transforms of Fourier type
42A45 Multipliers in one variable harmonic analysis
42A50 Conjugate functions, conjugate series, singularintegrals
42A55 Lacunary series of trigonometric and other functions; Riesz products
42A61 Probabilistic methods for one variable harmonicanalysis
42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
42A65 Completeness of sets of functions in one variableharmonic analysis
42A70 Trigonometric moment problems in one variableharmonic analysis 42A75 Classical almost periodic functions, mean periodic functions [See also 43A60]
42A82 Positive definite functions in one variable harmonic analysis
42A85 Convolution, factorization for one variable harmonic analysis
42A99 None of the above, but in this section
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42Axx 单变量谐波分析 42A50 共轭函数、共轭级数、奇异积分 |
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42Bxx Harmonic analysis in several variables {For automorphic theory, see mainly 11F30}
42B05 Fourier series and coefficients in several variables
42B08 Summability in several variables
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42B15 Multipliers for harmonic analysis in several vari-ables
42B20 Singular and oscillatory integrals (Calder´on-Zygmund, etc.)
42B25 Maximal functions, Littlewood-Paley theory
42B30 Hp -spaces
42B35 Function spaces arising in harmonic analysis
42B37 Harmonic analysis and PDEs [See also 35-XX]
42B99 None of the above, but in this section
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42Bxx 多变量谐波分析{关于自同构理论，主要参见 11F30} 42B05 多变量傅里叶级数与系数 42B08 多变量可加性 42B10 傅里叶变换与傅里叶-斯蒂尔杰斯变换其他傅里叶变换 42B15 多变量谐波分析乘法器 42B20 奇异与振荡积分（卡尔德隆-齐格蒙德，等) 42B25 最大函数，Littlewood-Paley理论 42B30 Hp-空格 42B35 调和分析中的函数空间 42B37 谐波分析与偏微分方程 [另见 35-XX] 42B99 本节不涉及上述内容 |
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42Cxx Nontrigonometric harmonic analysis
42C05 Orthogonal functions and polynomials, generaltheory of nontrigonometric harmonic analysis [Seealso 33C45, 33C50, 33D45]
42C10 Fourier series in special orthogonal functions(Legendre polynomials, Walsh functions, etc.)
42C15 General harmonic expansions, frames
42C20 Other transformations of harmonic type
42C25 Uniqueness and localization for orthogonal series42C30 Completeness of sets of functions in nontrigonometric harmonic analysis
42C40 Nontrigonometric harmonic analysis involvingwavelets and other special systems
42C99 None of the above, but in this section
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42Cxx 非三角函数谐波分析 42C05 正交函数与多项式，非三角调和分析的一般理论[另见33C45、33C50、33D45] 42C10 基于特殊正交函数的傅里叶级数(Legendre多项式、Walsh函数等) 42C15 一般调和展开式，框架 42C20 其他谐波型变换 42C25正交级数的唯一性与局部性42C30非三角函数集的完备性谐波分析 42C40 小波及其他特殊系统在非三角函数谐波分析中的应用 42C99 本节不涉及上述内容 |
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43-XX Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}
43-00 General reference works (handbooks, dictionaries,bibliographies, etc.) pertaining to abstract harmonic analysis
43-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to abstract harmonic analysis43-02 Research exposition (monographs, survey articles)pertaining to abstract harmonic analysis
43-03 History of abstract harmonic analysis [Consideralso classification numbers pertaining to Section 01]43-04 Software, source code, etc. for problems pertaining to abstract harmonic analysis
43-06 Proceedings, conferences, collections, etc. pertaining to abstract harmonic analysis
43-08 Computational methods for problems pertainingto abstract harmonic analysis
43-11 Research data for problems pertaining to abstractharmonic analysis
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43-XX 摘要谐波分析{关于拓扑学的其他分析 以及李群，参见22Exx} 43-00 涉及抽象调和的通用参考文献（手册、词典、书目等）分析 43-01 引言性阐述（教材、教程论文，等) 与抽象调和分析相关的研究阐述（专著、综述文章）43-02 与抽象调和分析相关的研究阐述 43-03 抽象调和分析史 [另请参阅第01节相关分类编号] 43-04 与问题相关的软件、源代码等抽象调和分析 43-06 会议记录、会议资料、文集等抽象调和分析 43-08 与抽象调和分析有关问题的计算方法 43-11 与抽象调和分析有关的问题的研究资料 |
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43Axx Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}
43A05 Measures on groups and semigroups, etc. 43A07 Means on groups, semigroups, etc.; amenable groups
43A10 Measure algebras on groups, semigroups, etc.
43A15 Lp -spaces and other function spaces on groups, semigroups, etc.
43A17 Analysis on ordered groups, Hp -theory
43A20 L1 -algebras on groups, semigroups, etc.
43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
43A32 Other transforms and operators of Fourier type
43A35 Positive definite functions on groups, semigroups, etc.
43A40 Character groups and dual objects
43A45 Spectral synthesis on groups, semigroups, etc.
43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
43A50 Convergence of Fourier series and of inverse transforms
43A55 Summability methods on groups, semigroups, etc. [See also 40J05]
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
43A62 Harmonic analysis on hypergroups
43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) [See also 22A10, 22A20, 22Dxx, 22E45]
43A70 Analysis on specific locally compact and other abelian groups [See also 11R56, 22B05]
43A75 Harmonic analysis on specific compact groups 43A77 Harmonic analysis on general compact groups
43A80 Analysis on other specific Lie groups [See also22Exx]
43A85 Harmonic analysis on homogeneous spaces 43A90 Harmonic analysis and spherical functions [Seealso 22E45, 22E46, 33C55]
43A95 Categorical methods for abstract harmonic analysis [See also 46Mxx]
43A99 None of the above, but in this section
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43Axx 摘要谐波分析{For 拓扑李代数的另一分析 群组，参见22Exx} 43A05 关于群与半群等的度量 43A07 关于群、半群等的定义负责的组 43A10 群、半群等上的测度代数 43A15 Lp群上的空间及其他函数空间半群等 43A17 有序群的分析，Hp-理论 43A20 L1群、半群等上的代数 43A22 同态与函数的乘子群、半群等上的空间 43A25局部傅里叶和傅里叶-斯蒂尔杰斯变换紧致群和其他阿贝尔群 43A30 非阿贝尔群上的傅里叶变换与傅里叶-斯蒂尔杰斯变换群和半群等。 43A32 其他傅里叶变换与运算符 43A35 群、半群上的正定函数等 43A40 字符组与双对象 43A45 群、半群等的谱合成 43A46 特殊集（薄集、克罗内克集、赫尔森集） 集合、Ditkin集合、Sidon集合等。) 43A50 傅里叶级数与逆傅里叶级数的收敛性改变 43A55 群、半群的可加性方法等[另见40J05]群与半群上的 43A60 几乎周期函数 以及它们的推广形式（递归函数，远端功能等)；几乎自同构的有或起作用 43A62 超群的调和分析 43A65 群、半群等的表示（方面）（抽象调和分析）[另见22A10、22A20、22Dxx、22E45] 43A70 局部紧致空间的分析及其他阿贝尔群 43A75 特定紧致群的调和分析 43A77 一般紧群的调和分析 43A80 其他特定李群的分析[另见22Exx] 43A85 同质空间上的调和分析 43A90 谐波分析与球面函数 [另见 22E45、22E46、33C55] 43A95 摘要调和分析的分类方法[另见46Mxx] 43A99 本节不涉及上述内容 |
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44-XX Integral transforms, operational calculus {For fractional derivatives and integrals, see
26A33; for Fourier transforms, see 42A38, 42B10; for integral transforms in distribution spaces, see 46F12; for numerical methods, see 65R10}
44-00 General reference works (handbooks, dictionaries,bibliographies, etc.) pertaining to integral transforms
44-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral transforms
44-02 Research exposition (monographs, survey articles)pertaining to integral transforms
44-03 History of integral transforms [Consider also classification numbers pertaining to Section 01]
44-04 Software, source code, etc. for problems pertaining to integral transforms
44-06 Proceedings, conferences, collections, etc. pertaining to integral transforms
44-11 Research data for problems pertaining to integraltransforms
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44-XX 积分变换，运算分式结石导数与积分，参见 26A33；关于傅里叶变换，请参阅42A38、42B10；用于整体转换分布空间 46F12；关于数值方法，参见65R10} 44-00 关于整体性转化的通用参考文献（手册、词典、书目等） 44-01 导论性阐述（教材、教程论文，等) 关于积分变换 44-02 研究性论文（专著、综述）：关于积分变换 44-03 积分变换的历史 [另见分类与第01节相关的数字 44-04 软件、源代码等相关问题积分变换 44-06 会议记录、会议资料、文集等积分变换 44-11 关于积分变换问题的研究数据 |
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44Axx Integral transforms, operational calculus {For fractional derivatives and in-tegrals,
see 26A33; for Fourier transforms, see 42A38, 42B10; for integral transforms in distribution spaces, see 46F12; for numerical methods, see 65R10}
44A05 General integral transforms [See also 42A38]
44A10 Laplace transform
44A12 Radon transform [See also 92C55]
44A15 Special integral transforms (Legendre, Hilbert, etc.)
44A20 Integral transforms of special functions
44A30 Multiple integral transforms
44A35 Convolution as an integral transform
44A40 Calculus of Mikusin´ski and other operational calculi
44A45 Classical operational calculus
44A55 Discrete operational calculus
44A60 Moment problems {For trigonometric moment problems, see 42A70}
44A99 None of the above, but in this section
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44Axx 积分变换，运算微积分{对于分数阶导数和积分，参见26A33；关于傅里叶变换，参见42A38、42B10；关于积分变换在分布空间中，参见46F12；关于数值方法，参见65R10} 44A05 一般积分变换 [另见 42A38] 44A10 拉普拉斯变换 44A12 氡变换[另见92C55] 44A15 特殊积分变换（Legendre、Hilbert）等 44A20 特殊函数的积分变换 44A30 多重积分变换 44A35 求积变换中的卷积 44A40 米库辛斯基计算及其他运算计算 44A45 经典运算学 44A55 离散运算演算 44A60 力矩问题 {针对三角函数力矩问题，参见2A70} 44A99 本节不涉及上述内容 |
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45-XX Integral equations
45-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral equations
45-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral equations
45-02 Research exposition (monographs, survey articles) pertaining to integral equations
45-03 History of integral equations [Consider also classification numbers pertaining to Section 01]
45-04 Software, source code, etc. for problems pertaining to integral equations
45-06 Proceedings, conferences, collections, etc. pertaining to integral equations
45-11 Research data for problems pertaining to integral equations
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45-XX 积分方程 45-00 通用参考文献（手册、词典、参考文献等)关于积分方程 45-01 导论性阐述（教材、教程论文，等) 积分方程 45-02 研究性论文（专著、综述文章）积分方程 45-03 积分方程的历史[另见分类]与第01节相关的数字 45-04 针对相关问题的软件、源代码等积分方程 45-06 会议记录、会议资料、文集等积分方程 45-11 关于积分问题的研究数据方程式 |
|
45Axx Linear integral equations
45A05 Linear integral equations
45A99 None of the above, but in this section
|
45Axx 线性积分方程 45A05 线性积分方程 45A99 本节不涉及上述内容 |
|
45Bxx Fredholm integral equations
45B05 Fredholm integral equations
45B99 None of the above, but in this section
|
45Bxx 弗雷德霍姆积分方程 45B05 弗雷德霍姆积分方程 45B99 本节不涉及上述内容 |
|
45Cxx Eigenvalue problems for integral equations [See also 34Lxx, 35Pxx, 45P05, 47A75]
45C05 Eigenvalue problems for integral equations [Seealso 34Lxx, 35Pxx, 45P05, 47A75]
45C99 None of the above, but in this section
|
45Cxx 积分的特征值问题方程[另见34Lxx、35Pxx、45P05]47A75] 45C05 积分方程的特征值问题 [另见 34Lxx、35Pxx、45P05、47A75] 45C99 本节不涉及上述内容 |
|
45Dxx Volterra integral equations [See also 34A12]
45D05 Volterra integral equations [See also 34A12]
45D99 None of the above, but in this sectio
|
45Dxx Volterra积分方程[参见也见34A12] 45D05 沃尔泰拉积分方程 [另见 34A12] 45D99 本节不涉及上述内容 |
|
45Exx Singular integral equations [See also 30E20, 30E25, 44A15, 44A35]
45E05 Integral equations with kernels of Cauchy type[See also 35J15]
45E10 Integral equations of the convolution type (Abel,Picard, Toeplitz and Wiener-Hopf type) [See also47B35]
45E99 None of the above, but in this section
|
45Exx 唯一积分方程 [另见30E20, 30E25, 44A15, 44A35] 45E05 Cauchy型核的积分方程[另见35J15] 45E10 积分型卷积方程（阿贝尔型、皮卡型、托普利茨型及维纳-霍普夫型）[另见47B35] 45E99 本节不涉及上述内容 |
|
45Fxx Systems of linear integral equations
45F05 Systems of nonsingular linear integral equations45F10 Dual, triple, etc., integral and series equations
45F15 Systems of singular linear integral equations
45F99 None of the above, but in this section
|
45Fxx 线性积分方程组 45F05 非奇异线性积分方程组45F10 对偶、三重等积分和级数方程 45F15奇异线性积分方程组 45F99 上述均非，但本节适用 |
|
45Gxx Nonlinear integral equations [See also 47H30, 47Jxx]
45G05 Singular nonlinear integral equations
45G10 Other nonlinear integral equations
45G15 Systems of nonlinear integral equations
45G99 None of the above, but in this section
|
45Gxx 非线性积分方程 [参见也包括 47H30、47Jxx] 45G05奇异非线性积分方程 45G10 其他非线性积分方程 45G15 非线性积分方程组 45G99 本节不涉及上述内容 |
|
45Hxx Integral equations with miscellaneous special kernels [See also 44A15]
45H05 Integral equations with miscellaneous special kernels [See also 44A15]
45H99 None of the above, but in this section
|
45Hxx 一元微分方程与杂项特殊内核 45H05 有各种特殊核的积分方程[另见44A15] 45H99 本节不涉及上述内容 |
|
45Jxx Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]
45J05 Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]
45J99 None of the above, but in this section
|
45Jxx 一阶常微分方程[另见34K05、34K30、47G20] 45J05 积分-常微分方程 [另见34K05, 34K30, 47G20] 45J99 本节不涉及上述内容 |
|
45Kxx Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
45K05 Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
45K99 None of the above, but in this section
|
45Kxx 积分-偏微分方程[另见 34K30、35R09、35R10、47G20] 45K05 整分偏微分方程 [另见34K30, 35R09, 35R10, 47G20] 45K99 本节不涉及上述内容 |
|
45Lxx Theoretical approximation of solutions to integral equations {For numerical analysis, see 65Rxx}
45L05 Theoretical approximation of solutions to integral equations {For numerical analysis, see 65Rxx}
45L99 None of the above, but in this section
|
45Lxx 解的理论近似关于积分方程{数值解分析，参见65Rxx} 45L05 积分解的理论近似方程{数值分析参见65Rxx} 45L99 本节不涉及上述内容 |
|
45Mxx Qualitative behavior of solutions to integral equations
45M05 Asymptotics of solutions to integral equations
45M10 Stability theory for integral equations
45M15 Periodic solutions of integral equations
45M20 Positive solutions of integral equations
45M99 None of the above, but in this section
|
45Mxx 溶液的定性行为积分方程 45M05 积分方程解的渐近性 45M10积分方程的稳定性理论 45M15 积分方程的周期解 45M20 积分方程的正解 45M99 本节不涉及上述内容 |
|
45Nxx Abstract integral equations, integral equations in abstract spaces
45N05 Abstract integral equations, integral equations in abstract spaces
45N99 None of the above, but in this section
|
45Nxx 摘要积分方程，积分抽象空间中的方程 45N05 摘要积分方程，积分方程在抽象空间 45N99 本节不涉及上述内容 |
|
45Pxx Integral operators [See also 47B38, 47G10]
45P05 Integral operators [See also 47B38, 47G10]
45P99 None of the above, but in this section
|
45Pxx 积分算子 [另见 47B38，47G10] 45P05 积分算子 [另见 47B38、47G10] 45P99 本节不涉及上述内容 |
|
45Qxx Inverse problems for integral equations
45Q05 Inverse problems for integral equations 45Q99 None of the above, but in this section
|
45Qxx 积分方程的反问题 45Q05积分方程的逆问题 45Q99 本节不涉及上述内容 |
|
45Rxx Random integral equations [See also 60H20]
45R05 Random integral equations [See also 60H20]
45R99 None of the above, but in this section
|
45Rxx 随机积分方程 [参见也 60H20] 45R05 随机积分方程 [另见 60H20] 45R99 本节不涉及上述内容 |
|
46-XX Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx}
46-00 General reference works (handbooks, dictionaries,bibliographies, etc.) pertaining to functional analysis
46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
46-02 Research exposition (monographs, survey articles)pertaining to functional analysis
46-03 History of functional analysis [Consider also classification numbers pertaining to Section 01]
46-04 Software, source code, etc. for problems pertaining to functional analysis
46-06 Proceedings, conferences, collections, etc. pertaining to functional analysis
46-08 Computational methods for problems pertainingto functional analysis
46-11 Research data for problems pertaining to functional analysis
|
46-XX 功能分析 {For 拓扑模型流形线性空间，见57Nxx，58Bxx 46-00 与功能分析相关的通用参考文献（手册、词典、参考书目等） 46-01 导论性阐述（教材、教程论文，等) 与功能分析有关 46-02 关于功能分析的研究性文献（专著、综述文章） 46-03 功能分析史 [另请参阅分类]与第01节相关的数字 46-04 针对相关问题的软件、源代码等功能分析 46-06 会议记录、会议资料、文集等功能分析 46-08 关于函数分析问题的计算方法 46-11 关于功能相关问题的研究数据分析 |
|
46Axx Topological linear spaces and related structures {For function spaces, see 46Exx}
46A03 General theory of locally convex spaces
46A04 Locally convex Fr´echet spaces and (DF)-spaces
46A08 Barrelled spaces, bornological spaces
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46A17 Bornologies and related structures; Mackey convergence, etc.
46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than R, etc.)
46A20 Duality theory for topological vector spaces
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]
46A25 Reflexivity and semi-reflexivity [See also 46B10]
46A30 Open mapping and closed graph theorems; completeness (including B-, Brompleteness)
46A32 Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]
46A35 Summability and bases in topological vector spaces [See also 46B15]
46A40 Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]
46A45 Sequence spaces (including K¨othe sequence spaces) [See also 46B45]
46A50 Compactness in topological linear spaces; angelic spaces, etc.
46A55 Convex sets in topological linear spaces; Choquet theory [See also 52A07]
46A61 Graded Fr´echet spaces and tame operators
46A63 Topological invariants ((DN), (Ω), etc.) for locally convex spaces
46A70 Saks spaces and their duals (strict topologies,mixed topologies, two-norm spaces, coSaks spaces,etc.)
46A80 Modular spaces
46A99 None of the above, but in this section
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46Axx拓扑线性空间及其相关问题结构 {关于函数空间，参见46埃克森} 46A03 局部凸空间的一般理论 46A04局部凸Fréchet空间与(DF)空间 46A08 管状空间，诞生学空间 46A11 由紧致性或可加性决定的间距性质（核空间、Schwartz空间，蒙特勒空间等) 46A13 由归纳极限或射影极限定义的空间（LB、LF等）[另见46M40] 46A16 非局部凸空间（可度量拓扑学）线性空间，局部有界空间，拟巴拿赫空间空间等) 46A17 生物学与相关结构；麦基收敛性等 46A19 其他“拓扑”线性空间（收敛性）空间、排序空间、具有度量的空比R更通用的有序结构中的值 等) 46A20 代数向量空间的对偶理论 46A22 Hahn-Banach型定理；推广与泛函与算子的提升[另见46M10] 46A25 反射性与半反射性 [另见 46B10] 46A30 开映射与闭图定理；完全性（包括B-、Br-完整性） 46A32 线性算子的空间；拓扑张量产品；逼近性质[另见46B28, 46M05, 47L05, 47L20] 46A35 代数和与拓扑向量基间隙[另见46B15] 46A40 有序拓扑线性空间，向量格[另见 06F20、46B40、46B42] 46A45 序列空间（包括K¨othe序列空间）[另见46B45] 46A50 拓扑线性空间中的紧致性；天使空间等 46A55 拓扑线性空间中的凸集；Choquet理论[另见52A07] 46A61 分级Fréchet空间与驯化算子 46A63 拓扑不变量 ((DN)，(Ω) 等。) 用于本地凸空间 46A70 Saks空间及其对偶（严格拓扑、混合拓扑、双范数空间、余Saks空间等） 46A80 模块化空间 46A99 本节不涉及上述内容 |
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46Cxx Inner product spaces and their generalizations, Hilbert spaces {For function
spaces, see 46Exx}
46C05 Hilbert and preHilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35]
46C15 Characterizations of Hilbert spaces
46C20 Spaces with indefinite inner product (Kre˘ın spaces, Pontryagin spaces, etc.) [See also 47B50]
46C50 Generalizations of inner products (semiinner products, partial inner products, etc.)
46C99 None of the above, but in this section
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46Cxx 内积空间及其推广希尔伯特空间{关于函数 空间，见46Exx} 46C05 希尔伯特空间与前希尔伯特空间：几何学与 拓扑学（包括具有半定内积的空间产品 46C07 希尔伯特子空间（=算子值域）；补空间 （阿隆萨因、德·布兰热等）[另见46B70, 46M35] 46C15希尔伯特空间的特征 46C20 内积不定的空间 (Kre ın 空间、庞特里亚金空间等。) [另见47B50] 46C50 内积的推广（半内积）乘积、部分内积等。) 46C99 本节不涉及上述内容 |
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46Exx Linear function spaces and their duals [See also 30H05, 32A38, 46F05] {For
function algebras, see 46J10}
46E05 Lattices of continuous, differentiable or analytic functions
46E10 Topological linear spaces of continuous, differentiable or analytic functions
46E15 Banach spaces of continuous, differentiable or analytic functions
46E20 Hilbert spaces of continuous, differentiable or analytic functions
46E22 Hilbert spaces with reproducing kernels (=(proper) functional Hilbert spaces, including de
Branges-Rovnyak and other structured spaces) [See also 47B32]
46E25 Rings and algebras of continuous, differentiable or analytic functions {For Banach function algbras, see 46J10, 46J15}
46E27 Spaces of measures [See also 28A33, 46Gxx]
46E30 Spaces of measurable functions (Lp-spaces, Or-licz spaces, K¨othe function spaces, Lorentz spaces,rearrangement invariant spaces, ideal spaces, etc.)46E35 Sobolev spaces and other spaces of “smooth”functions, embedding theorems, trace theorems
46E36 Sobolev (and similar kinds of) spaces of functionson metric spaces; analysis on metric spaces
46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
46E40 Spaces of vector- and operator-valued functions
46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20,46G25, 47H60] 46E99 None of the above, but in this section
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46Exx 线性函数空间及其对偶[另见30H05、32A38、46F05] {关于函数代数，参见46J10} 46E05 连续、可微或解析的格点有或起作用 46E10 连续可微的拓扑线性空间或解析函数 46E15 连续、可微或解析的Banach空间有或起作用 46E20 连续可微或解析的希尔伯特空间有或起作用 46E22 有再生核的希尔伯特空间（=（适当的）函数希尔伯特空间，包括Branges-Rovnyak及其他结构化空间）[参见也见于47B32] 46E25 连续可微的环与代数或解析函数{对于Banach函数代数，见46J10、46J15 46E27 测度空间 [另见 28A33、46Gxx] 46E30 可测函数空间（Lp-空格，Or-licz 空间、K¨othe函数空间、洛伦兹空间、重排不变空间、理想空间等。)46E35 Sobolev空间及其他“光滑”函数空间、嵌入定理、迹定理 46E36 Sobolev（及类似）度量空间上的函数空间；度量空间上的分析 46E39 索博列夫（及类似）离散变量函数空间 46E40 向量值函数与算子值函数空间 46E50 可微函数或全纯函数空间 在无限维空间中[另见46G20、46G25、47H60] 46E99 本节不涉及上述内容 |
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46Fxx Distributions, generalized functions, distribution spaces [See also 46T30]
46F05 Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10,46E35]
46F10 Operations with distributions and generalizedfunctions
46F12 Integral transforms in distribution spaces [Seealso 42-XX, 44-XX]
46F15 Hyperfunctions, analytic functionals [See also32A25, 32A45, 32C35, 58J15]
46F20 Distributions and ultradistributions as boundaryvalues of analytic functions [See also 30D40, 30E25,32A40]
46F25 Distributions on infinite-dimensional spaces [Seealso 58C35]
46F30 Generalized functions for nonlinear analysis(Rosinger, Colombeau, nonstandard, etc.)
46F99 None of the above, but in this section
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46Fxx 分布，广义函数，分布空间 46F05 测试函数、分布的拓扑线性空间及超分布[另见46E10、46E35] 46F10 分布与广义函数运算 46F12 分布空间中的积分变换 [另见 42-XX，44-XX] 46F15 超函数，解析泛函 [另见32A25、32A45、32C35、58J15] 46F20 分布与超分布作为解析函数的边界值 [另见 30D40、30E25、32A40] 46F25 无限维空间上的分布[另见58C35] 46F30 非线性分析的广义函数（Rosinger、Colombeau、非标准等） 46F99 本节不涉及上述内容 |
|
46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional
spaces) [See also 28-XX, 46Txx]
46G05 Derivatives of functions in infinite-dimensionalspaces [See also 46T20, 58C20, 58C25]
46G10 Vector-valued measures and integration [See also28Bxx, 46B22]
46G12 Measures and integration on abstract linearspaces [See also 28C20, 46T12]
46G15 Functional analytic lifting theory [See also28A51]
46G20 Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]
46G25 (Spaces of) multilinear mappings, polynomials[See also 46E50, 46G20, 47H60]
46G99 None of the above, but in this section
|
46Gxx 测量、集成、导数全态性（均涉及无限维 空间）[另见28-XX，46Txx] 46G05 无限维空间中函数的导数 [另见 46T20, 58C20, 58C25] 46G10 向量值测度与积分 [另见28Bxx，46B22] 46G12 抽象线性空间的度量与积分 [另见28C20, 46T12] 46G15 功能分析性提升理论 [另见28A51] 46G20 无限维全纯性 [另见 32-XX、46E50、46T25、58B12、58C10] 46G25（空间的）多元线性映射，多项式[另见46E50、46G20、47H60] 46G99 本节不涉及上述内容 |
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46Hxx Topological algebras, normed rings and algebras, Banach algebras {For group
algebras, convolution algebras and measure algebras, see 43A10, 43A20}
46H05 General theory of topological algebras
46H10 Ideals and subalgebras
46H15 Representations of topological algebras
46H20 Structure, classification of topological algebras
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46H30 Functional calculus in topological algebras [See also 47A60]
46H35 Topological algebras of operators [See mainly
47Lxx]
46H40 Automatic continuity
46H70 Nonassociative topological algebras [See also
46K70, 46L70]
46H99 None of the above, but in this section
|
46Hxx 拓扑代数，赋范环以及代数，Banach代数{关于群 46H05 拓扑代数通论 46H10 理想与子代数 46H15 代数的拓扑表示 46H20 代数结构与拓扑代数的分类 46H25 标准模与巴拿赫模，拓扑学模块（若未置于13-XX或16-XX中） 46H30 拓扑代数中的泛函分析 [参见也见于47A60] 46H35 算子的拓扑代数 [主要参见47Lxx] 46H40 自动连续性 46H70 非结合拓扑代数 [另见46K70, 46L70] 46H99 本节不涉及上述内容 |
|
46Jxx Commutative Banach algebras and commutative topological algebras [See also
46E25]
46J05 General theory of commutative topological algebras
46J10 Banach algebras of continuous functions, functionalgebras [See also 46E25]
46J15 Banach algebras of differentiable or analytic functions, Hp -spaces [See also 30H10, 32A35, 32A37,32A38, 42B30]
46J20 Ideals, maximal ideals, boundaries
46J25 Representations of commutative topological algebras
46J30 Subalgebras of commutative topological algebras46J40 Structure and classification of commutative topological algebras
46J45 Radical Banach algebras
46J99 None of the above, but in this section
|
46Jxx 交换Banach代数与交换拓扑代数[另见46E25] 46J05 交换拓扑代数的一般理论 46J10 连续函数的巴拿赫代数 46J15 可微或解析函数的Banach代数=高能 -空格 [另见 30H10、32A35、32A37、32A38、42B30] 46J20 理想，极大理想，边界 46J25 交换拓扑代数的表示 46J30 交换拓扑代数的子代数46J40交换拓扑代数的结构与分类代数 46J45 激进巴拿赫代数 46J99 本节不涉及上述内容 |
|
46Kxx Topological (rings and) algebras with an involution [See also 16W10]
46K05 General theory of topological algebras with involution
46K10 Representations of topological algebras with involution
46K15 Hilbert algebras
46K50 Nonselfadjoint (sub)algebras in algebras with involution
46K70 Nonassociative topological algebras with an involution [See also 46H70, 46L70]
46K99 None of the above, but in this section
|
46Kxx 代数拓扑学伴退化[另见16W10] 46K05 代数拓扑的对合一般理论 46K10 具有对合的拓扑代数的表示 46K15 希尔伯特代数 46K50 代数中的非自伴（子）代数 46K70 具有对合的非结合拓扑代数[另见46H70、46L70] 46K99 本节不涉及上述内容 |
|
46Lxx Selfadjoint operator algebras (C∗-algebras, von Neumann (W∗-) algebras,etc.) [See also 22D25, 47Lxx]
46L05 General theory of C∗-algebras
46L06 Tensor products of C∗-algebras
46L07 Operator spaces and completely bounded maps[See also 47L25]
46L08 C∗-modules
46L09 Free products of C∗-algebras
46L10 General theory of von Neumann algebras
46L30 States of selfadjoint operator algebras
46L35 Classifications of C∗-algebras
46L36 Classification of factors
46L37 Subfactors and their classification
46L40 Automorphisms of selfadjoint operator algebras
46L45 Decomposition theory for C∗-algebras
46L51 Noncommutative measure and integration
46L52 Noncommutative function spaces
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
46L55 Noncommutative dynamical systems [See also28Dxx, 37Kxx, 37Lxx, 37A55]
46L57 Derivations, dissipations and positive semigroupsin C∗-algebras
46L60 Applications of selfadjoint operator algebras tophysics [See also 46N50, 46N55, 47L90, 81T05,82B10, 82C10]
46L65 Quantizations, deformations for selfadjoint operator algebras
46L67 Quantum groups (operator algebraic aspects)
46L70 Nonassociative selfadjoint operator algebras [Seealso 46H70, 46K70]
46L80 K-theory and operator algebras (including cyclictheory) [See also 18F25, 19Kxx, 46M20, 55Rxx,58J22]
46L85 Noncommutative topology [See also 58B32,58B34, 58J22]
46L87 Noncommutative differential geometry [See also58B32, 58B34, 58J22]
46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also 58B32, 58B34, 58J22]
46L99 None of the above, but in this section
|
46Lxx自伴算子代数（C∗-代数，冯·诺依曼（W∗-) 代数， |
|
46Mxx Methods of category theory in
functional analysis [See also 18-XX]
46M05 Tensor products in functional analysis [See also46A32, 46B28, 47A80]
46M07 Ultraproducts in functional analysis [See also46B08, 46S20]
46M10 Projective and injective objects in functionalanalysis [See also 46A22]
46M15 Categories, functors in functional analysis {ForK-theory, Ext, etc., see 19K33, 46L80, 46M18,46M20}
46M18 Homological methods in functional analysis (ex-act
sequences, right inverses, lifting, etc.)
46M20 Methods of algebraic topology in functionalanalysis (cohomology, sheaf and bundle theory, etc.)[See also 14F06, 18Fxx, 19Kxx, 32Cxx, 32Lxx,46L80, 46M15, 46M18, 55Rxx]
46M35 Abstract interpolation of topological vectorspaces [See also 46B70]
46M40 Inductive and projective limits in functionalanalysis [See also 46A13]
46M99 None of the above, but in this section
|
46Mxx 范畴论方法功能分析[另见18-XX] 46M05 函数分析中的张量积 [另见46A32、46B28、47A80] 46M07 超产品在功能分析中的应用[另见46B08、46S20] 46M10 函数分析中的射影与单射对象 [另见 46A22] 46M15范畴、泛函分析中的函子{ForK理论、Ext等，参见19K33、46L80、46M18、46M20} 46M18 功能分析中的同源方法（ex-act）序列、右逆、提升等) 46M20 函数分析中的代数拓扑方法（包括上同调、层论与丛论等）[另见14F06、18Fxx、19Kxx、32Cxx、32Lxx、46L80、46M15、46M18、55Rxx] 46M35 拓扑向量空间的抽象插值[另见46B70] 46M40 函数分析中的诱导极限与投影极限 [另见 46A13] 46M99 本节不涉及上述内容 |
|
46Nxx Miscellaneous applications of functional analysis [See also 47Nxx]
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming,economics
46N20 Applications of functional analysis to differentialand integral equations
46N30 Applications of functional analysis in probabilitytheory and statistics
46N40 Applications of functional analysis in numericalanalysis [See also 65Jxx]
46N50 Applications of functional analysis in quantumphysics
46N55 Applications of functional analysis in statisticalphysics
46N60 Applications of functional analysis in biology andother sciences
46N99 None of the above, but in this section
|
46Nxx 功能性杂项应用分析[另见47Nxx] 46N10 功能分析在优化中的应用凸分析 46N20 用泛函分析方法求解微分方程和积分方程 46N30 《概率论与统计》中的泛函分析应用 46N40 功能分析在数值分析中的应用 [另见 65Jxx] 46N50 功能分析在量子物理中的应用 46N55 功能分析在统计物理学中的应用 46N60 功能分析在生物学及其他科学中的应用 46N99 本节不涉及上述内容 |
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46Sxx Other (nonclassical) types of functional analysis [See also 47Sxx]
46S05 Quaternionic functional analysis
46S10 Functional analysis over fields other than R orC or the quaternions; non-Archimedean functionalanalysis [See also 12J25, 32P05]
46S20 Nonstandard functional analysis [See also 03H05]46S30 Constructive functional analysis [See also 03F60]
46S40 Fuzzy functional analysis [See also 03E72] 46S50 Functional analysis in probabilistic metric linearspaces
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50, 58C50]
46S99 None of the above, but in this section
|
46Sxx 其他（非经典）功能类型分析[另见47Sxx] 46S05 四元数泛函分析 46S10 除R、C或四元数外的其他域的功能分析；非阿基米德函数分析[另见12J25,32P05] 46S20 非标准功能分析 [另见 03H05] 46S30 构造性功能分析 [另见 03F60] 46S40 模糊功能分析 [另见 03E72] 46S50 概率度量线性空间中的函数分析 46S60 超空间（超流形）的功能分析或分级空间[另见58A50、58C50] 46S99 本节不涉及上述内容 |
|
46Txx Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]
46T05 Infinite-dimensional manifolds [See also 53Axx,57N20, 58Bxx, 58Dxx]
46T10 Manifolds of mappings
46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds[See also 28Cxx, 46G12, 60-XX]
46T20 Continuous and differentiable maps in nonlinearfunctional analysis [See also 46G05]
46T25 Holomorphic maps in nonlinear functional analysis [See also 46G20]
46T30 Distributions and generalized functions on nonlinear spaces [See also 46Fxx]
46T99 None of the above, but in this section
|
46Txx 非线性功能分析 [参见以及 47Hxx、47Jxx、58Cxx、58Dxx] 46T05 无限维流形 [另见 53Axx，57N20,58Bxx，58Dxx] 46T10 映射的流形 46T12 测量（高斯、圆柱体等）与积分（费曼、路径、菲涅耳等）在流形上的应用[另见28Cxx、46G12、60-XX] 46T20 非线性泛函分析中的连续可微映射 [另见 46G05] 46T25非线性泛函分析中的全纯映射[另见46G20] 46T30 非线性分布与泛函间隙 46T99 本节不涉及上述内容 |
|
47-XX Operator theory
47-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operator theory
47-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
47-03 History of operator theory [Consider also classification numbers pertaining to Section 01]
47-04 Software, source code, etc. for problems pertaining to operator theory
47-06 Proceedings, conferences, collections, etc. pertaining to operator theory
47-08 Computational methods for problems pertainingto operator theory
47-11 Research data for problems pertaining to operatortheory
|
47-XX 运算子理论 47-00 通用参考文献（手册、词典、参考文献等) 运算子理论 47-01 引言性阐述（教材、教程论文，等) 运算子理论 47-02 研究性论文（专著、综述文章）算子论 47-03 算子理论史 [另见分类与第01节相关的数字 47-04 针对相关问题的软件、源代码等算子论 47-06 会议记录、会议资料、文集等算子论 47-08 运算子理论相关问题的计算方法 47-11 运算子理论相关问题的研究数据 |
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47Axx General theory of linear operators
47A05 General (adjoints, conjugates, products, inverses,domains, ranges, etc.)
47A06 Linear relations (multivalued linear operators)
47A07 Forms (bilinear, sesquilinear, multilinear)
47A08 Operator matrices [See also 47A13]
47A10 Spectrum, resolvent
47A11 Local spectral properties of linear operators
47A12 Numerical range, numerical radius
47A13 Several-variable operator theory (spectral, Fred-holm, etc.)
47A15 Invariant subspaces of linear operators [See also47A46]
47A16 Cyclic vectors, hypercyclic and chaotic operators47A20 Dilations, extensions, compressions of linear op-erators
47A25
Spectral sets of linear operators
47A30 Norms (inequalities, more than one norm, etc.)of linear operators
47A35 Ergodic theory of linear operators [See also28Dxx, 37Axx]
47A40 Scattering theory of linear operators [See also34L25, 35P25, 37K15, 58J50, 81Uxx]
47A45 Canonical models for contractions and nonselfad-joint linear operators
47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
47A48 Operator colligations (= nodes), vessels, linearsystems, characteristic functions, realizations, etc.
47A50 Equations and inequalities involving linear operators, with vector unknowns
47A52 Linear operators and ill-posed problems, regularization [See also 35R25, 47J06, 65F22, 65J20,65L08, 65M30, 65R30]
47A53 (Semi-) Fredholm operators; index theories [Seealso 58B15, 58J20]
47A55 Perturbation theory of linear operators [See also47H14, 58J37, 70H09, 81Q15]
47A56 Functions whose values are linear operators(operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
47A57 Linear operator methods in interpolation, moment and extension problems [See also 30E05,42A70, 42A82, 44A60]
47A58 Linear operator approximation theory
47A60 Functional calculus for linear operators
47A62 Equations involving linear operators, with operator unknowns
47A63 Linear operator inequalities
47A64 Operator means involving linear operators,shorted linear operators, etc.
47A65 Structure theory of linear operators
47A66 Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators
47A67 Representation theory of linear operators
47A68 Factorization theory (including Wiener-Hopf andspectral factorizations) of linear operators
47A70 (Generalized) eigenfunction expansions of linearoperators; rigged Hilbert spaces
47A75 Eigenvalue problems for linear operators [See also47J10, 49R05]
47A80 Tensor products of linear operators [See also46M05]
47A99 None of the above, but in this section
|
47Axx 线性算子的一般理论 47A05 一般（伴随、共轭、乘积、逆、定义域、值域等） 47A06 线性关系（多值线性算子） 47A07 表式（双线性、三线性、多线性） 47A08 运算符矩阵 [另见 47A13] 47A10 谱，消解剂 47A11 线性算子的局部谱性质 47A12 数值范围，数值半径 47A13 多变量算子理论（谱论、Fredholm）等) 47A15 线性算子的不变子空间 [另见47A46] 47A16 循环向量、超循环与混沌算子47A20 线性算子的扩张、延拓与压缩 47A25 线性算子的谱集 47A30 线性算子的范数（不等式、多重范数等） 47A35 线性算子的遍历理论 [另见28Dxx，37Axx]本节不涉及上述内容 47A40 线性算子散射理论 [另见34L25、35P25、37K15、58J50、81Uxx] 47A45 反缩与非自同构的典范模型线性算子 47A46 投射链（巢）或不变子空间链 沿链积分等 47A48 运算符对合（=节点）、容器、线性系统、特征函数、实现等。 47A50 涉及线性算子的方程与不等式 带向量未知数的 47A52 线性算子与不适定问题，正则化[另见35R25、47J06、65F22、65J20、65L08、65M30、65R30] 47A53（半）Fredholm算子；指标理论[另见58B15、58J20] 47A55 线性算子的微扰理论 [另见47H14、58J37、70H09、81Q15] 47A56 值为线性算子的函数（包括算子值函数、矩阵值函数等）解析和亚纯函数 47A57 插值中的线性算子方法及延伸问题[另见30E05、42A70、42A82、44A60] 47A58 线性算子逼近理论 47A60 线性算子的泛函分析 47A62 涉及线性算子的方程，带有算子不知名或不出名的人 47A63 线性算子不等式 47A64 操作符指涉及线性操作符、短路线性操作符等。 47A65 线性算子的结构理论 47A66 类三角形与非类三角形类对角形 非拟对角线性算子 47A67 线性算子的表示论 47A68 线性算子的因子分解理论（包括维纳-霍普夫因子分解和谱因子分解） 47A70（广义）线性算子的本征函数展开；受约束的希尔伯特空间 47A75 线性算子的特征值问题 [另见47J10、49R05] 47A80 线性算子的张量积 [另见46M05] 47A99 本节不涉及上述内容 |
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47Bxx Special classes of linear operators
47B01 Operators on Banach spaces
47B02 Operators on Hilbert spaces (general)
47B06 Riesz operators; eigenvalue distributions; approximation
numbers, s-numbers, Kolmogorovnumbers, entropy numbers, etc. of operators
47B07 Linear operators defined by compactness proper-ties
47B10
Linear operators belonging to operator ideals
47B07 Linear operators defined by compactness proper-ties
47B10
Linear operators belonging to operator ideals(nuclear, p-summing, in the Schatten-von Neumannclasses, etc.) [See also 47L20]
47B12 Sectorial operators
47B13 Cowen-Douglas operators
47B15 Hermitian and normal operators (spectral mea-sures,
functional calculus, etc.)
47B25 Linear symmetric and selfadjoint operators (unbounded)47B20 Subnormal operators, hyponormal operators, etc. 47B28 Nonselfadjoint operators [See also 47A45, 81Q12] 47B32 Linear operators in reproducing-kernel Hilbertspaces (including de Branges, de Branges-Rovnyak,and other structured spaces) [See also 46E22] 47B33 Linear composition operators 47B34 Kernel operators 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators {For other integral operators, seealso 45P05, 47G10} [See also 32A25, 32M15] 47B36 Jacobi (tridiagonal) operators (matrices) andgeneralizations 47B37 Linear operators on special spaces (weightedshifts, operators on sequence spaces, etc.) 47B38 Linear operators on function spaces (general) 47B39 Linear difference operators [See also 39A70] 47B40 Spectral operators, decomposable operators,well-bounded operators, etc. 47B44 Linear accretive operators, dissipative operators,etc. 47B47 Commutators, derivations, elementary operators,etc. 47B48 Linear operators on Banach algebras 47B49 Transformers, preservers (linear operators onspaces of linear operators) 47B50 Linear operators on spaces with an indefinitemetric [See also 46C20] 47B60 Linear operators on ordered spaces 47B65 Positive linear operators and order-bounded operators 47B80 Random linear operators [See also 47H40, 60H25]47B90 Operator theory and harmonic analysis [See also42-XX, 43-XX, 44-XX] 47B91 Operators on complex function spaces 47B92 Operators on real function spaces 47B93 Operators arising in mathematical physics 47B99 None of the above, but in this section |
47Bxx 线性算子的特殊类 47B01 禁闭空间上的算子 47B02 离子-电子体系中的算符（一般） 47B06 Riesz算子；特征值分布；逼近算子的数、s-数、柯尔莫哥洛夫数、熵数等 47B07 由紧致性定义的线性算子 47B10 属于算子理想（核算子、p-和算子、Schatten-von Neumann类等）的线性算子[另见47L20] 47B12 部门运营商 47B13 科恩-道格拉斯算子 47B15 哈密顿算子与正规算子（谱测度，函数演算等) 47B20 亚正规算子、次正规算子等。 47B25 线性对称和自伴随算子（无界） 47B28 非自伴算子 [另见 47A45,81Q12] 47B32 重构核希尔伯特空间中的线性算子（包括德布朗格空间、德布朗格-罗夫尼亚克空间及其他结构化空间）[另见 46E22] 47B33 线性组合算子 47B34 核算符 47B35 Toeplitz算子，Hankel算子，Wiener-Hopf 算子{其他积分算子参见45P05、47G10} [另见32A25、32M15] 47B36 Jacobi（三对角）算子（矩阵）及其推广 47B37 特殊空间上的线性算子（加权移位、序列空间上的算子等） 47B38 函数空间上的线性算子（一般） 47B39 线性差分算子 [另见 39A70] 47B40 谱算子、可分解算子、良有界算子等。 47B44 线性增殖算子、耗散算子等。 47B47 交换机、导联、基本操作符等。 47B48 Banach代数上的线性算子 47B49 变换器，保函（线性算子的线性算子空间） 47B50 无限度量空间上的线性算子[另见46C20] 47B60 有序空间上的线性算子 47B65 正线性算子与序有界算子 47B80 随机线性算子 [另见 47H40、60H25] 47B90 算子理论与调和分析 [另见 42-XX、43-XX、44-XX] 47B91 复函数空间上的算子 47B92实函数空间上的算子 47B93 数学物理中的算子 47B99 本节不涉及上述内容 |
|
47Cxx Individual linear operators as elements of algebraic systems
47C05 Linear operators in algebras
47C10 Linear operators in ∗-algebras
47C15 Linear operators in C∗- or von Neumann algebras
47C99 None of the above, but in this section |
47Cxx 作为元素的个体线性算子代数系统 47C05 代数中的线性算子 47C10 线性算子∗-代数 47C15 C语言中的线性算子∗- 或冯·诺依曼代数 47C99 本节不涉及上述内容 |
|
47Dxx Groups and semigroups of linear operators, their generalizations and appli-cations
47D03
Groups and semigroups of linear operators [Seealso 20M20] {For nonlinear operators, see 47H20}47D06 One-parameter semigroups and linear evolutionequations [See also 34G10, 34K30]
47D07 Markov semigroups and applications to diffusionprocesses {For Markov processes, see 60Jxx}
47D08 Schr¨odinger and Feynman-Kac semigroups
47D09 Operator sine and cosine functions and higher-order
Cauchy problems [See also 34G10]
47D60 C-semigroups, regularized semigroups
47D62 Integrated semigroups
47D99 None of the above, but in this section
|
47Dxx 线性群与半群算子及其推广与应用 47D03 线性算子的群与半群[另见20M20]{关于非线性算子，参见47H20} 47D06 一参数半群与线性演化方程[另见34G10、34K30] 47D07 马尔可夫半群及其在扩散过程中的应用 {关于马尔可夫过程，参见60Jxx} 47D08薛定谔和费曼-卡茨半群 47D09 操作正弦、余弦函数及高阶函数柯西问题 47D60 C半群，正则化半群 47D62 一体化半群 47D99 本节不涉及上述内容 |
|
47Exx Ordinary differential operators [See also 34Bxx, 34Lxx]
47E05 General theory of ordinary differential operators(should also be assigned at least one other classifica-tion
number in Section 47) [See also 34Bxx, 34Lxx]
47E07 Functional-differential and differential-difference operators [See also 34K08] 47E99 None of the above, but in this section
|
47Exx 普通微分算子 [参见也包括34Bxx、34Lxx] 47E05 常微分算子的一般理论（还应至少指定一个其他分类）第47节中的数字）[另见34Bxx、34Lxx] 47E07 函数微分算子与微分差分算子 [另见34K08] 47E99 本节不涉及上述内容 |
|
47Fxx Partial differential operators [See also 35Pxx, 58Jxx]
47F05 General theory of partial differential operators(should also be assigned at least one other classifica-tion
number in Section 47) [See also 35Pxx, 58Jxx]47F10 Elliptic operators and their generalizations {Forelliptic complexes, see 58J10}
47F99 None of the above, but in this section
|
47Fxx偏微分算子[参见也包括35Pxx、58Jxx] 47F05偏微分算子通论（还应至少指定一个其他分类） 第47节中的数字）[另见35Pxx、58Jxx]47F10 椭圆算子及其推广{关于椭圆复形，参见58J10} 47F99 本节不涉及上述内容 |
|
47Gxx Integral, integro-differential, and pseudodifferential operators [See also 58Jxx]
47G10 Integral operators [See also 45P05] 47G20 Integro-differential operators [See also 34K30,35R09, 35R10, 45Jxx, 45Kxx]
47G30 Pseudodifferential operators [See also 35Sxx,58Jxx]
47G40 Potential operators [See also 31-XX]
47G99 None of the above, but in this section
|
47Gxx积分、积分微分及伪微分算子 [另见58Jxx] 47G10 积分算子 [另见 45P05] 47G20 整分算子 [另见 34K30,35R09,35R10,45Jxx，45Kxx] 47G30 假微分算子 [另见 35Sxx，58Jxx] 47G40 潜在操作员 [另见 31-XX] 47G99 本节不涉及上述内容 |
|
47Hxx Nonlinear operators and their properties {For global and geometric aspects, see 49J53, 58-XX, especially
58Cxx}
47H04 Set-valued operators [See also 28B20, 54C60,58C06]
47H05 Monotone operators and generalizations
47H06 Nonlinear accretive operators, dissipative operators, etc.
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vectorspaces
47H08 Measures of noncompactness and condensingmappings, K-set contractions, etc.
47H09 Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.
47H10 Fixed-point theorems [See also 37C25, 54H25,55M20, 58C30]
47H11 Degree theory for nonlinear operators [See also55M25, 58C30]
47H14 Perturbations of nonlinear operators [See also47A55, 58J37, 70H09, 70K60, 81Q15]
47H20 Semigroups of nonlinear operators [See also37L05, 47J35, 54H15, 58D07]
47H25 Nonlinear ergodic theorems [See also 28Dxx,37Axx, 47A35]
47H30 Particular nonlinear operators (superposition,Hammerstein, Nemytski˘ı, Uryson, etc.) [See also45Gxx, 45P05]
47H40 Random nonlinear operators [See also 47B80,60H25]
47H60 Multilinear and polynomial operators [See also46G25]
47H99 None of the above, but in this section
|
47Hxx 非线性算子及其属性 {用于全局和几何相关方面，参见49J53、58-XX，特别是58Cxx} 47H20 非线性算子半群 [另见37L05、47J35、54H15、58D07] |
|
47Jxx Equations and inequalities involving nonlinear operators [See also 46Txx] {For global and geometric aspects, see 58-XX}
47J05 Equations involving nonlinear operators (general)[See also 47H10, 47J25]
47J06 Nonlinear ill-posed problems [See also 35R25,47A52, 65F22, 65J20, 65L08, 65M30, 65R30]
47J07 Abstract inverse mapping and implicit functiontheorems involving nonlinear operators [See also46T20, 58C15]
47J10 Nonlinear spectral theory, nonlinear eigenvalueproblems [See also 49R05]
47J15 Abstract bifurcation theory involving nonlinearoperators [See also 34C23, 37Gxx, 58E07, 58E09]
47J20 Variational and other types of inequalities involv-ing
nonlinear operators (general) [See also 49J40]
47J22 Variational and other types of inclusions [See also34A60, 49J21, 49K21]
47J25 Iterative procedures involving nonlinear operators[See also 47J26, 65J15]
47J26 Fixed-point iterations [See also 47J25]
47J30 Variational methods involving nonlinear opera-tors
[See also 58Exx]
47J35 Nonlinear evolution equations [See also 34G20,35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx,47H20, 58D25]
47J40 Equations with nonlinear hysteresis operators[See also 34C55, 74N30]
47J99 None of the above, but in this section
|
47Hxx 非线性算子及其属性 {用于全局和几何相关方面，参见49J53、58-XX，特别是58Cxx}
47H20 非线性算子半群 [另见37L05、47J35、54H15、58D07] |
|
47Lxx Linear spaces and algebras of operators [See also 46Lxx]
47L05 Linear spaces of operators [See also 46A32,46B28]
47L07 Convex sets and cones of operators [See also46A55]
47L10 Algebras of operators on Banach spaces and other topological linear spaces
47L15 Operator algebras with symbol structure
47L20 Operator ideals [See also 47B10]
47L22 Ideals of polynomials and of multilinear mappingsin operator theory
47L25 Operator spaces (= matricially normed spaces)[See also 46L07]
47L30 Abstract operator algebras on Hilbert spaces
47L35 Nest algebras, CSL algebras
47L40 Limit algebras, subalgebras of C∗-algebras
47L45 Dual algebras; weakly closed singly generated operator algebras
47L50 Dual spaces of operator algebras
47L55 Representations of (nonselfadjoint) operator algebras
47L65 Crossed product algebras (analytic crossed products)
47L70 Nonassociative nonselfadjoint operator algebras
47L75 Other nonselfadjoint operator algebras
47L80 Algebras of specific types of operators (Toeplitz,integral, pseudodifferential, etc.)
47L90 Applications of operator algebras to the sciences47L99 None of the above, but in this sectio
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47Lxx 线性空间与算子代数[另见46Lxx] 47L05 线性算子空间 [另见 46A32,46B28] 47L07 算子的凸集与锥 [另见46A55] 47L10 班纳赫空间和其他拓扑线性空间上的算子代数带符号结构的 47L15 算子代数 47L20 操作员理想 [另见 47B10] 47L22 算子论中多项式与多重线性映射的理想 47L25 算子空间（=矩阵赋范空间）[另见46L07] 47L30 希尔伯特空间上的抽象算子代数 47L35 巢代数，CSL代数 47L40 有限代数，C的子代数∗-代数 47L45 二元代数；弱闭单生成算子代数 47L50算子代数的双空间 47L55（非自伴）算子代数的表示 47L65 交叉积代数（解析交叉积） 47L70 非结合非自伴算子代数 47L75 其他非自伴算子代数 47L80 特定算子类型的代数（Toeplitz、积分、伪微分等） 47L90 运算子代数在科学中的应用 47L99 本节不涉及上述内容 |
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47Nxx Miscellaneous applications of operator theory [See also 46Nxx]
47N10 Applications of operator theory in optimization,convex analysis, mathematical programming, economics
47N20 Applications of operator theory to differentialand integral equations
47N30 Applications of operator theory in probabilitytheory and statistics
47N40 Applications of operator theory in numericalanalysis [See also 65Jxx]
47N50 Applications of operator theory in the physicalsciences
47N60 Applications of operator theory in chemistry andlife sciences
47N70 Applications of operator theory in systems, signals, circuits, and control theory
47N99 None of the above, but in this section
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47Nxx 运算符的其他应用理论[另见46Nxx] 47N10 算子理论在优化、凸分析、数学规划、经济学中的应用 47N20 算子理论在微分方程和积分方程中的应用 47N30算子论在概率论和统计中的应用 47N40算子论在数值分析中的应用[另见65Jxx] 47N50算子论在物理科学中的应用 47N60算子理论在化学和生命科学中的应用 47N70 系统与信号中的算子理论应用电路与控制理论 47N99 本节不涉及上述内容 |
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47Sxx Other (nonclassical) types of operator theory [See also 46Sxx]
47S05 Quaternionic operator theory
47S10 Operator theory over fields other than R, C orthe quaternions; non-Archimedean operator theory47S20 Nonstandard operator theory [See also 03H05]
47S30 Constructive operator theory [See also 03F60]
47S40 Fuzzy operator theory [See also 03E72]
47S50 Operator theory in probabilistic metric linearspaces [See also 54E70]
47S99 None of the above, but in this section
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47Sxx 其他（非经典）类型的操作员理论[另见46Sxx] 47S05 四元数算子理论 47S10 除实数域、复数域或四元数域外的算子理论；非阿基米德算子理论47S20 非标准算子理论[另见03H05] 47S30 构造算子理论 [另见 03F60] 47S40 模糊算子理论 [另见 03E72] 47S50 概率度量线性空间中的算子理论 [另见 54E70] 47S99 本节不涉及上述内容 |
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49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx,
93-XX]
49-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to calculus of vari-ations
and optimal control
49-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
49-02 Research exposition (monographs, survey articles)pertaining to calculus of variations and optimal control
49-03 History of calculus of variations and optimal control [Consider also classification numbers pertainingto Section 01]
49-04 Software, source code, etc. for problems pertaining to calculus of variations and optimal control
49-06 Proceedings, conferences, collections, etc. pertaining to calculus of variations and optimal control
49-11 Research data for problems pertaining to calculus of variations and optimal control |
49-XX 变分法与最优控制；优化[参见还有34H05、34K35、65Kxx、90Cxx 93-XX] 49-00 通用参考文献（手册、词典、参考文献等变分法最优控制 49-01 引言性阐述（教材、教程论文，等) 与变分法相关最优控制 49-02 变分法与最优控制研究进展（专著、综述） 49-03 变分法与最优控制的历史[另请参阅第01章节的分类编号] 49-04 变分法与最优控制相关问题的软件、源代码等 49-06 与变分法和最优控制相关的会议论文集、会议记录、文集等 49-11 变分法与最优控制问题的研究数据 |
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49Jxx Existence theories in calculus of variations and optimal control
49J05 Existence theories for free problems in one independent variable
49J10 Existence theories for free problems in two ormore independent variables
49J15 Existence theories for optimal control problemsinvolving ordinary differential equations
49J20 Existence theories for optimal control problemsinvolving partial differential equations
49J21 Existence theories for optimal control problemsinvolving relations other than differential equations
49J27 Existence theories for problems in abstract spaces[See also 90C48, 93C25] 49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
49J35 Existence of solutions for minimax problems
49J40 Variational inequalities [See also 47J20]
49J45 Methods involving semicontinuity and convergence; relaxation
49J50 Fr´echet and Gateaux differentiability in optimization [See also 46G05, 58C20]
49J52 Nonsmooth analysis [See also 46G05, 58C50,90C56]
49J53 Set-valued and variational analysis [See also28B20, 47H04, 54C60, 58C06]
49J55 Existence of optimal solutions to problems involving randomness [See also 93E20]
49J99 None of the above, but in this section
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49Jxx 微积分中的存在性理论变分与最优控制 49J05 单独立变量自由问题的存在性理论 49J10 两个或多个自变量自由问题的存在性理论 49J15 涉及常微分方程的最优控制问题的存在性理论 49J20 涉及偏微分方程的最优控制问题的存在性理论 49J21 涉及非微分方程关系的最优控制问题存在性理论 49J27 抽象空间问题的存在性理论[另见90C48、93C25] 49J30 属于受限的最优解的存在性类别（Lipschitz控制、bang-bang控制） 等) 49J35极小极大问题解的存在性 49J40 变分不等式 [另见 47J20] 49J45 涉及半连续性和收敛性的方法；消遣 49J50 Fr‘echet与Gateaux可微性在优化中的应用[另见46G05、58C20] 49J52 非光滑分析 [另见 46G05、58C50、90C56] 49J53 集值分析与变分分析 [另见28B20、47H04、54C60、58C06] 49J55 涉及问题的最优解的存在性随机性[另见93E20] 49J99 本节不涉及上述内容 |
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49Kxx Optimality conditions
49K05 Optimality conditions for free problems in oneindependent variable
49K10 Optimality conditions for free problems in two ormore independent variables
49K15 Optimality conditions for problems involving ordinary differential equations
49K20 Optimality conditions for problems involvingpartial differential equations
49K21 Optimality conditions for problems involving relations other than differential equations
49K27 Optimality conditions for problems in abstractspaces [See also 90C48, 93C25]
49K30 Optimality conditions for solutions belongingto restricted classes (Lipschitz controls, bang-bangcontrols, etc.)
49K35 Optimality conditions for minimax problems
49K40 Sensitivity, stability, well-posedness [See also90C31]
49K45 Optimality conditions for problems involvingrandomness [See also 93E20]
49K99 None of the above, but in this section
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49Kxx 最优性条件单变量自由问题的最优性条件2个或更多独立变量下自由问题的最优性条件 49K15 涉及或有概率问题的最优性条件微分方程 49K20 偏微分方程问题的最优性条件 49K21 关于涉及关系问题的最优性条件 微分方程之外的 49K27 抽象空间中问题的最优性条件[另见90C48、93C25] 49K30 属于受限类（Lipschitz控制、bang-bang控制等）解的最优性条件 49K35 最小极大问题的最优性条件 49K40 灵敏性、稳定性、适定性 [另见90C31] 49K45 涉及随机性的问题的最优性条件[另见93E20] 49K99 本节不涉及上述内容 |
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49Lxx Hamilton-Jacobi theories [See also70H20, 35F21]
49L12 Hamilton-Jacobi equations in optimal control and differential games
49L20 Dynamic programming in optimal control anddifferential games
49L25 Viscosity solutions to Hamilton-Jacobi equationsin optimal control and differential games
49L99 None of the above, but in this section
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49Lxx Hamilton-Jacobi理论[另见70H20, 35F21] 49L12 最优控制与微分博弈中的Hamilton-Jacobi方程 49L20 最优控制与微分博弈中的动态规划 49L25 最优控制与微分博弈中Hamilton-Jacobi方程的粘性解 49L99 本节不涉及上述内容 |
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49Mxx Numerical methods in optimal control[See also 65Kxx, 90-08, 90Cxx]
49M05 Numerical methods based on necessary conditions
49M15 Newton-type methods [See also 90C53]
49M20 Numerical methods of relaxation type
49M25 Discrete approximations in optimal control
49M27 Decomposition methods
49M29 Numerical methods involving duality
49M37 Numerical methods based on nonlinear programming [See also 65Kxx, 90C30]
49M41 PDE constrained optimization (numerical as-pects)
49M99 None of the above, but in this section
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49Mxx 最优控制中的数值方法[另见 65Kxx、90-08、90Cxx] 49M05 基于必要条件的数值方法 49M15 牛顿型方法 49M20 放松型数值方法 49M25 最优控制中的离散逼近 49M27 分解方法 49M29 涉及对偶性的数值方法 49M37基于非线性规划的数值计算方法[另见 65Kxx，90C30] 49M41 PDE约束优化（数值方面） 49M99 本节不涉及上述内容 |
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49Nxx Miscellaneous topics in calculus of variations and optimal control
49N05 Linear optimal control problems [See also 93C05]49N10 Linear-quadratic optimal control problems
49N15 Duality theory (optimization) [See also 90C46]
49N20 Periodic optimal control problems
49N25 Impulsive optimal control problems
49N30 Problems with incomplete information (optimization)[See also 93C41]
49N35 Optimal feedback synthesis [See also 93B52]
49N45 Inverse problems in optimal control
49N60 Regularity of solutions in optimal control
49N70 Differential games and control [See also 91A23]49N75 Pursuit and evasion games [See also 91A24]
49N80 Mean field games and control [See also 91A16]
49N90 Applications of optimal control and differentialgames [See also 90C90, 91A80, 93C95]
49N99 None of the above, but in this section
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49Nxx 微积分中的杂题变分与最优控制 49N05 线性最优控制问题 [另见 93C05]49N10 线性-二次最优控制问题 49N15 对偶理论（优化）[另见 90C46] 49N20周期最优控制问题 49N25 脉冲最优控制问题 49N30 不完全信息问题（优化）[另见93C41] 49N35 最佳反馈合成 [另见 93B52] 49N45 最优控制中的逆问题 49N60 最优控制中解的正则性 49N70 差分游戏与控制 [另见 91A23]49N75 追击与躲避游戏 [另见 91A24] 49N80 平均场游戏与控制 [另见 91A16] 49N90 最优控制与微分博弈的应用 [另见 90C90、91A80、93C95] 49N99 本节不涉及上述内容 |
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49Qxx Manifolds and measure-geometric topics [See also 58Exx]
49Q05 Minimal surfaces and optimization [See also53A10, 58E12]
49Q10 Optimization of shapes other than minimal surfaces[See also 90C90]
49Q12 Sensitivity analysis for optimization problems onmanifolds
49Q15 Geometric measure and integration theory, integral and normal currents in optimization [See also28A75, 32C30, 58A25, 58C35]
49Q20 Variational problems in a geometric measure-theoretic setting
49Q22 Optimal transportation [See also 90B06]
49Q99 None of the above, but in this section
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49Qxx 管道与测量几何主题 |
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49Rxx Variational methods for eigenvalues of operators (should also be assigned at least one other classification number in Section 49) [See also 47A75]
49R05 Variational methods for eigenvalues of operators(should also be assigned at least one other classifi-cation
number in Section 49) [See also 47A75]
49R99 None of the above, but in this section
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49Rxx 特征值的变分方法操作符（亦应被分配至少一个其他分类编号在 第49条）[另见47A75] 49R05 算子特征值的变分方法（还应至少被归入另一类） 第49条中的数字）[另见47A75] 49R99 本节不涉及上述内容 |
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49Sxx Variational principles of physics (should also be assigned at least one other classification number in Section 49)
49S05 Variational principles of physics (should also beassigned at least one other classification number inSection 49)
49S99 None of the above, but in this section
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49Sxx 物理变分原理（还应至少分配另一个第49条分类编号) 49S05 物理变分原理（该课程还应在第49章中至少分配另一个分类编号） 49S99 本节不涉及上述内容 |
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